Combined Feed
https://feeds.library.caltech.edu/people/Simmons-Duffin-D/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 01:55:53 +0000Assessing alternatives for directional detection of a halo of weakly interacting massive particles
https://resolver.caltech.edu/CaltechAUTHORS:20170817-113427429
Authors: {'items': [{'id': 'Copi-C-J', 'name': {'family': 'Copi', 'given': 'Craig J.'}}, {'id': 'Krauss-L-M', 'name': {'family': 'Krauss', 'given': 'Lawrence M.'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Stroiney-S-R', 'name': {'family': 'Stroiney', 'given': 'Steven R.'}}]}
Year: 2007
DOI: 10.1103/PhysRevD.75.023514
The future of direct terrestrial WIMP detection lies on two fronts: new, much larger low background detectors sensitive to energy deposition, and detectors with directional sensitivity. The former can explore a large range of WIMP parameter space using well-tested technology while the latter may be necessary if one is to disentangle particle physics parameters from astrophysical halo parameters. Because directional detectors will be quite difficult to construct it is worthwhile exploring in advance generally which experimental features will yield the greatest benefits at the lowest costs. We examine the sensitivity of directional detectors with varying angular tracking resolution with and without the ability to distinguish forward versus backward recoils, and compare these to the sensitivity of a detector where the track is projected onto a two-dimensional plane. The latter detector regardless of where it is placed on the Earth, can be oriented to produce a significantly better discrimination signal than a 3D detector without this capability, and with sensitivity within a factor of 2 of a full 3D tracking detector. Required event rates to distinguish signals from backgrounds for a simple isothermal halo range from the low teens in the best case to many thousands in the worst.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qz8ab-t7t78Quark and Lepton Flavor Physics from F-Theory
https://resolver.caltech.edu/CaltechAUTHORS:20170817-082611073
Authors: {'items': [{'id': 'Randall-L', 'name': {'family': 'Randall', 'given': 'Lisa'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2009
DOI: 10.48550/arXiv.0904.1584
Recent work on local F-theory models shows the potential for new categories of flavor models. In this paper we investigate the perturbative effective theory interpretation of this result. We also show how to extend the model to the neutrino sector.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/n5mrq-yez70Superconformal flavor simplified
https://resolver.caltech.edu/CaltechAUTHORS:20170815-131911295
Authors: {'items': [{'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2010
DOI: 10.1007/JHEP05(2010)079
A simple explanation of the flavor hierarchies can arise if matter fields interact with a conformal sector and different generations have different anomalous dimensions under the CFT. However, in the original study by Nelson and Strassler many supersymmetric models of this type were considered to be 'incalculable' because the R-charges were not sufficiently constrained by the superpotential. We point out that nearly all such models are calculable with the use of a-maximization. Utilizing this, we construct the simplest vector-like flavor models and discuss their viability. A significant constraint on these models comes from requiring that the visible gauge couplings remain perturbative throughout the conformal window needed to generate the hierarchies. However, we find that there is a small class of simple flavor models that can evade this bound.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/k76f9-46418Bounds on 4D conformal and superconformal field theories
https://resolver.caltech.edu/CaltechAUTHORS:20170816-075019110
Authors: {'items': [{'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2011
DOI: 10.1007/JHEP05(2011)017
We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N = 1 superconformal field theories. In any CFT containing a scalar primary ϕ of dimension d we show that crossing symmetry of ⟨ϕϕϕϕ⟩ implies a completely general lower bound on the central charge c ≥ f_c(d). Similarly, in CFTs containing a complex scalar charged under global symmetries, we bound a combination of symmetry current two-point function coefficients τ^(IJ) and flavor charges. We extend these bounds to N = 1 superconformal theories by deriving the superconformal block expansions for four-point functions of a chiral superfield Φ and its conjugate. In this case we derive bounds on the OPE coefficients of scalar operators appearing in the Φ × Φ^† OPE, and show that there is an upper bound on the dimension of Φ^†Φ when dim Φ is close to 1. We also present even more stringent bounds on c and τ^(IJ). In supersymmetric gauge theories believed to flow to superconformal fixed points one can use anomaly matching to explicitly check whether these bounds are satisfied.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1g2nz-r8y56Effective conformal theory and the flat-space limit of AdS
https://resolver.caltech.edu/CaltechAUTHORS:20170816-092357056
Authors: {'items': [{'id': 'Fitzpatrick-A-L', 'name': {'family': 'Fitzpatrick', 'given': 'A. Liam'}}, {'id': 'Katz-Emanuel', 'name': {'family': 'Katz', 'given': 'Emanuel'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2011
DOI: 10.1007/JHEP07(2011)023
We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, O, we consider the anomalous dimensions, γ(n,l), of the double-trace operators of the form O(∂^2)^n(∂)^lO. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of |γ(n,l)| < 4. Non-renormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the
heavy field "unitarizes" the growth in the anomalous dimensions, and leads to a resonance like behavior in γ(n, l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in d-dimensional CFTs and flatspace S-matrix elements in d + 1 dimensions. We comment on the emergence of flat-space locality from the CFT perspective.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1z96r-0cm02N = 1 SQCD and the transverse field Ising model
https://resolver.caltech.edu/CaltechAUTHORS:20170815-104135691
Authors: {'items': [{'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2012
DOI: 10.1007/JHEP02(2012)009
We study the dimensions of non-chiral operators in the Veneziano limit of N = 1 supersymmetric QCD in the conformal window. We show that when acting on gauge-invariant operators built out of scalars, the 1-loop dilatation operator is equivalent to the spin chain Hamiltonian of the 1D Ising model in a transverse magnetic field, which is a nontrivial integrable system that is exactly solvable at finite length. Solutions with periodic boundary conditions give the anomalous dimensions of flavor-singlet operators and solutions with fixed boundary conditions give the anomalous dimensions of operators whose ends contain open flavor indices.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2zzd0-r0j89Jet physics from static charges in AdS space
https://resolver.caltech.edu/CaltechAUTHORS:20170817-113523187
Authors: {'items': [{'id': 'Chien-Yang-Ting', 'name': {'family': 'Chien', 'given': 'Yang-Ting'}}, {'id': 'Schwartz-Matthew-D', 'name': {'family': 'Schwartz', 'given': 'Matthew D.'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Stewart-I-W', 'name': {'family': 'Stewart', 'given': 'Iain W.'}}]}
Year: 2012
DOI: 10.1103/PhysRevD.85.045010
Soft interactions with high-energy jets are explored in radial coordinates which exploit the approximately conformal behavior of perturbative gauge theories. In these coordinates, the jets, approximated by Wilson lines, become static charges in Euclidean AdS. The anomalous dimension of the corresponding Wilson line operator is then determined by the potential energy of the charges. To study these Wilson lines we introduce a "conformal gauge" which does not have kinetic mixing between radial and angular directions, and show that a number of properties of Wilson lines are reproduced through relatively simple calculations. For example, certain nonplanar graphs involving multiple Wilson lines automatically vanish. We also discuss the linear growth of the charges' imaginary potential energy with separation, and a relationship between Wilson line diagrams and Witten diagrams.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/v8337-ka575Carving out the space of 4D CFTs
https://resolver.caltech.edu/CaltechAUTHORS:20170816-080350610
Authors: {'items': [{'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Vichi-Alessandro', 'name': {'family': 'Vichi', 'given': 'Alessandro'}}]}
Year: 2012
DOI: 10.1007/JHEP05(2012)110
We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N = 1 superconformal field theories. Using our algorithm, we dramatically improve previous bounds on a number of CFT quantities, particularly for theories with global symmetries. In the case of SO(4) or SU(2) symmetry, our bounds severely constrain models of conformal technicolor. In N = 1 superconformal theories, we place strong bounds on dim(Φ^†Φ), where Φ is a chiral operator. These bounds asymptote to the line dim(Φ^†Φ) ≤ 2 dim(Φ) near dim(Φ) ≃ 1, forbidding positive anomalous dimensions in this region. We also place novel upper and lower bounds on OPE coefficients of protected operators in the Φ × Φ OPE. Finally, we find examples of lower bounds on central charges and flavor current two-point functions that scale with the size of global symmetry representations. In the case of N = 1 theories with an SU(N) flavor symmetry, our bounds on current two-point functions lie within an O(1) factor of the values realized in supersymmetric QCD in the conformal window.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3qjj4-1r595Solving the 3D Ising model with the conformal bootstrap
https://resolver.caltech.edu/CaltechAUTHORS:20170817-113623391
Authors: {'items': [{'id': 'El-Showk-Sheer', 'name': {'family': 'El-Showk', 'given': 'Sheer'}}, {'id': 'Paulos-M-F', 'name': {'family': 'Paulos', 'given': 'Miguel F.'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Rychkov-Slava', 'name': {'family': 'Rychkov', 'given': 'Slava'}, 'orcid': '0000-0002-5847-1011'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Vichi-Alessandro', 'name': {'family': 'Vichi', 'given': 'Alessandro'}}]}
Year: 2012
DOI: 10.1103/PhysRevD.86.025022
We study the constraints of crossing symmetry and unitarity in general 3D conformal field theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for their computation in arbitrary space-time dimension. Comparing the resulting bounds on operator dimensions and product-expansion coefficients in 3D to known results, we find that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space. We also derive general upper bounds on the dimensions of higher spin operators, relevant in the context of theories with weakly broken higher spin symmetries.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fpg8c-qv360The analytic bootstrap and AdS superhorizon locality
https://resolver.caltech.edu/CaltechAUTHORS:20170817-080656583
Authors: {'items': [{'id': 'Fitzpatrick-A-L', 'name': {'family': 'Fitzpatrick', 'given': 'A. Liam'}}, {'id': 'Kaplan-Jared', 'name': {'family': 'Kaplan', 'given': 'Jared'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2013
DOI: 10.1007/JHEP12(2013)004
We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| ≪ |υ| < 1. We prove that every CFT with a scalar operator ϕ must contain infinite sequences of operators O_(τ,ℓ) with twist approaching τ → 2Δ_ϕ + 2n for each integer n as ℓ → ∞. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the ϕ × ϕ OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as ℓ → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/awzre-jpy32Projectors, shadows, and conformal blocks
https://resolver.caltech.edu/CaltechAUTHORS:20170815-121618494
Authors: {'items': [{'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2014
DOI: 10.1007/JHEP04(2014)146
We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the "shadow formalism" of Ferrara, Gatto, Grillo, and Parisi in a setting where conformal invariance is manifest. Conformal blocks in d-dimensions can be expressed as integrals over the projective null-cone in the "embedding space" R^(Rd+1,1). Taking care with their analytic structure, these integrals can be evaluated in great generality, reducing the computation of conformal blocks to a bookkeeping exercise. To facilitate calculations in four-dimensional CFTs, we introduce techniques for writing down conformally-invariant correlators using auxiliary twistor variables, and demonstrate their use in some simple examples.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/03jye-wam98Conformal Field Theories in Fractional Dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20170817-113742628
Authors: {'items': [{'id': 'El-Showk-Sheer', 'name': {'family': 'El-Showk', 'given': 'Sheer'}}, {'id': 'Paulos-M-F', 'name': {'family': 'Paulos', 'given': 'Miguel'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Rychkov-Slava', 'name': {'family': 'Rychkov', 'given': 'Slava'}, 'orcid': '0000-0002-5847-1011'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Vichi-Alessandro', 'name': {'family': 'Vichi', 'given': 'Alessandro'}}]}
Year: 2014
DOI: 10.1103/PhysRevLett.112.141601
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary conformal field theories connecting the 2D Ising model, the 3D Ising model, and the free scalar theory in 4D. We give numerical predictions for the leading operator dimensions and central charge in this family at different values of D and compare these to calculations of ϕ^4 theory in the ϵ expansion.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/07rnp-awn62Bootstrapping the O(N) vector models
https://resolver.caltech.edu/CaltechAUTHORS:20170816-085543194
Authors: {'items': [{'id': 'Kos-Filip', 'name': {'family': 'Kos', 'given': 'Filip'}, 'orcid': '0000-0001-7332-1655'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2014
DOI: 10.1007/JHEP06(2014)091
We study the conformal bootstrap for 3D CFTs with O(N ) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N ) singlet and symmetric tensor operators appearing in the ϕ_i × ϕ_j OPE, where ϕ_i is a fundamental of O(N). Comparing these bounds to previous determinations of critical exponents in the O(N) vector models, we find strong numerical evidence that the O(N) vector models saturate the bootstrap constraints at all values of N. We also compute general lower bounds on the central charge, giving numerical predictions for the values realized in the O(N) vector models. We compare our predictions to previous computations in the 1/N expansion, finding precise agreement at large values of N.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/304xn-6dw81N = 1 superconformal blocks for general scalar operators
https://resolver.caltech.edu/CaltechAUTHORS:20170816-094432377
Authors: {'items': [{'id': 'Khandker-Z-U', 'name': {'family': 'Khandker', 'given': 'Zuhair U.'}}, {'id': 'Li-Daliang', 'name': {'family': 'Li', 'given': 'Daliang'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2014
DOI: 10.1007/JHEP08(2014)049
We use supershadow methods to derive new expressions for superconformal blocks in 4d N = 1 superconformal field theories. We analyze the four-point function ⟨A_1A^†_2B_1B^†_2⟩, where A_i and ℬ_i are scalar superconformal primary operators with arbitrary dimension and R-charge and the exchanged operator is neutral under R-symmetry. Previously studied superconformal blocks for chiral operators and conserved currents are special cases of our general results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/qvdk2-8ab07Covariant approaches to superconformal blocks
https://resolver.caltech.edu/CaltechAUTHORS:20170816-100454243
Authors: {'items': [{'id': 'Fitzpatrick-A-L', 'name': {'family': 'Fitzpatrick', 'given': 'A. Liam'}}, {'id': 'Kaplan-Jared', 'name': {'family': 'Kaplan', 'given': 'Jared'}}, {'id': 'Khandker-Z-U', 'name': {'family': 'Khandker', 'given': 'Zuhair U.'}}, {'id': 'Li-Daliang', 'name': {'family': 'Li', 'given': 'Daliang'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2014
DOI: 10.1007/JHEP08(2014)129
We develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions containing chiral operators in theories with NN -extended supersymmetry. We also reproduce these results by extending the "shadow formalism" of Ferrara, Gatto, Grillo, and Parisi to supersymmetric theories, where superconformal blocks can be represented as superspace integrals of three-point functions multiplied by shadow three-point functions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dp5yw-za741Bootstrapping mixed correlators in the 3D Ising model
https://resolver.caltech.edu/CaltechAUTHORS:20170816-100454795
Authors: {'items': [{'id': 'Kos-Filip', 'name': {'family': 'Kos', 'given': 'Filip'}, 'orcid': '0000-0001-7332-1655'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2014
DOI: 10.1007/JHEP11(2014)109
We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a ℤ_2 global symmetry. For the leading ℤ_2-odd operator σ and ℤ_2-even operator ϵ, we obtain numerical constraints on the allowed dimensions (Δ_σ, Δ_ϵ) assuming that σ and ϵ are the only relevant scalars in the theory. These constraints yield a small closed region in (Δ_σ, Δ_ϵ) space compatible with the known values in the 3D Ising CFT.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1kty1-dmr30Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
https://resolver.caltech.edu/CaltechAUTHORS:20170816-100455664
Authors: {'items': [{'id': 'El-Showk-Sheer', 'name': {'family': 'El-Showk', 'given': 'Sheer'}}, {'id': 'Paulos-M-F', 'name': {'family': 'Paulos', 'given': 'Miguel F.'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Rychkov-Slava', 'name': {'family': 'Rychkov', 'given': 'Slava'}, 'orcid': '0000-0002-5847-1011'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Vichi-Alessandro', 'name': {'family': 'Vichi', 'given': 'Alessandro'}}]}
Year: 2014
DOI: 10.1007/s10955-014-1042-7
We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z_2 -even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Δ_σ=0.518154(15), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/65v19-7hc54A semidefinite program solver for the conformal bootstrap
https://resolver.caltech.edu/CaltechAUTHORS:20170816-085746505
Authors: {'items': [{'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2015
DOI: 10.1007/JHEP06(2015)174
We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite program solver, designed for the conformal bootstrap. SDPB significantly outperforms less specialized solvers and should enable many new computations. As an example application, we compute a new rigorous high-precision bound on operator dimensions in the 3d Ising CFT, Δ_σ = 0.518151(6), Δ_ϵ = 1.41264(6).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/msspm-ynf53Bootstrapping the O(N) archipelago
https://resolver.caltech.edu/CaltechAUTHORS:20170816-100455073
Authors: {'items': [{'id': 'Kos-Filip', 'name': {'family': 'Kos', 'given': 'Filip'}, 'orcid': '0000-0001-7332-1655'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Vichi-A', 'name': {'family': 'Vichi', 'given': 'Alessandro'}}]}
Year: 2015
DOI: 10.1007/JHEP11(2015)106
We study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N) vector ϕi and the lowest dimension O(N) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions (Δ_ϕ, Δ_s) to lie inside small islands. We also make rigorous determinations of current two-point functions in the O(2) and O(3) models, with applications to transport in condensed matter systems.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3r1p7-5ar41Bootstrapping 3D fermions
https://resolver.caltech.edu/CaltechAUTHORS:20170815-114833470
Authors: {'items': [{'id': 'Iliesiu-Luca', 'name': {'family': 'Iliesiu', 'given': 'Luca'}, 'orcid': '0000-0001-7567-7516'}, {'id': 'Kos-Filip', 'name': {'family': 'Kos', 'given': 'Filip'}, 'orcid': '0000-0001-7332-1655'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Pufu-S-S', 'name': {'family': 'Pufu', 'given': 'Silviu S.'}, 'orcid': '0000-0001-8316-9589'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Yacoby-Ran', 'name': {'family': 'Yacoby', 'given': 'Ran'}}]}
Year: 2016
DOI: 10.1007/JHEP03(2016)120
We study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C_T. We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N . We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dz3tp-tat27Fermion-scalar conformal blocks
https://resolver.caltech.edu/CaltechAUTHORS:20170815-123720250
Authors: {'items': [{'id': 'Iliesiu-Luca', 'name': {'family': 'Iliesiu', 'given': 'Luca'}, 'orcid': '0000-0001-7567-7516'}, {'id': 'Kos-Filip', 'name': {'family': 'Kos', 'given': 'Filip'}, 'orcid': '0000-0001-7332-1655'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Pufu-S-S', 'name': {'family': 'Pufu', 'given': 'Silviu S.'}, 'orcid': '0000-0001-8316-9589'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Yacoby-Ran', 'name': {'family': 'Yacoby', 'given': 'Ran'}}]}
Year: 2016
DOI: 10.1007/JHEP04(2016)074
We compute the conformal blocks associated with scalar-scalar-fermion-fermion 4-point functions in 3D CFTs. Together with the known scalar conformal blocks, our result completes the task of determining the so-called 'seed blocks' in three dimensions. Conformal blocks associated with 4-point functions of operators with arbitrary spins can now be determined from these seed blocks by using known differential operators.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/baq2r-kqm82The conformal bootstrap
https://resolver.caltech.edu/CaltechAUTHORS:20170817-111715996
Authors: {'items': [{'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2016
DOI: 10.1038/nphys3761
The conformal bootstrap was proposed in the 1970s as a strategy for calculating the properties of second-order phase transitions. After spectacular success elucidating two-dimensional systems, little progress was made on systems in higher dimensions until a recent renaissance beginning in 2008. We report on some of the main results and ideas from this renaissance, focusing on new determinations of critical exponents and correlation functions in the three-dimensional Ising and O(N) models.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/wky85-5z220Precision islands in the Ising and O(N ) models
https://resolver.caltech.edu/CaltechAUTHORS:20170816-100454531
Authors: {'items': [{'id': 'Kos-Filip', 'name': {'family': 'Kos', 'given': 'Filip'}, 'orcid': '0000-0001-7332-1655'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Vichi-Alessandro', 'name': {'family': 'Vichi', 'given': 'Alessandro'}}]}
Year: 2016
DOI: 10.1007/JHEP08(2016)036
We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, (Δ_σ, Δ_ϵ, λ_(σσϵ), λ_(ϵϵϵ)) = (0.5181489(10), 1.412625(10), 1.0518537(41), 1.532435(19) , give the most precise determinations of these quantities to date.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9qv8p-zbv52Looking for a bulk point
https://resolver.caltech.edu/CaltechAUTHORS:20170815-102514589
Authors: {'items': [{'id': 'Maldacena-Juan', 'name': {'family': 'Maldacena', 'given': 'Juan'}, 'orcid': '0000-0002-9127-1687'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Zhiboedov-Alexander', 'name': {'family': 'Zhiboedov', 'given': 'Alexander'}}]}
Year: 2017
DOI: 10.1007/JHEP01(2017)013
We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xdyhz-jk553Non-gaussianity of the critical 3d Ising model
https://resolver.caltech.edu/CaltechAUTHORS:20170817-113958355
Authors: {'items': [{'id': 'Rychkov-S', 'name': {'family': 'Rychkov', 'given': 'Slava'}, 'orcid': '0000-0002-5847-1011'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Zan-B', 'name': {'family': 'Zan', 'given': 'Bernardo'}, 'orcid': '0000-0002-5218-5540'}]}
Year: 2017
DOI: 10.21468/SciPostPhys.2.1.001
We discuss the 4pt function of the critical 3d Ising model, extracted from recent conformal bootstrap results. We focus on the non-gaussianity Q - the ratio of the 4pt function to its gaussian part given by three Wick contractions. This ratio reveals significant non-gaussianity of the critical fluctuations. The bootstrap results are consistent with a rigorous inequality due to Lebowitz and Aizenman, which limits Q to lie between 1/3 and 1.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6q7ep-qkf95The lightcone bootstrap and the spectrum of the 3d Ising CFT
https://resolver.caltech.edu/CaltechAUTHORS:20170419-081614629
Authors: {'items': [{'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2017
DOI: 10.1007/JHEP03(2017)086
We compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2, RR ) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an asymptotic expansion in large spin, and suggest a strategy for going beyond the large spin limit. We carry out the first steps of this strategy for the 3d Ising CFT, deriving analytic approximations for the dimensions and OPE coefficients of several infinite families of operators in terms of the initial data {Δ_σ, Δ_ϵ, f_(σσϵ), f_(ϵϵϵ), c_T}. The analytic results agree with numerics to high precision for about 100 low-twist operators (correctly accounting for O(1) mixing effects between large-spin families). Plugging these results back into the crossing equations, we obtain approximate analytic constraints on the initial data.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/jb552-xtc84The random-bond Ising model in 2.01 and 3 dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20170817-110229744
Authors: {'items': [{'id': 'Komargodski-Z', 'name': {'family': 'Komargodski', 'given': 'Zohar'}, 'orcid': '0000-0002-8486-0811'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2017
DOI: 10.1088/1751-8121/aa6087
We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2 < d < 4 this disorder is a relevant perturbation that drives the system to a new fixed point of the renormalization group. At d = 2 such disorder is marginally irrelevant and can be studied using conformal perturbation theory. Combining conformal perturbation theory with recent results from the conformal bootstrap we compute some scaling exponents in an expansion around d = 2. If one trusts these computations also in d = 3, one finds results consistent with experimental data and Monte Carlo simulations. In addition, we perform a direct uncontrolled computation in d = 3 using new results for low-lying operator dimensions and OPE coefficients in the 3d Ising model. We compare these new methods with previous studies. Finally, we comment about the O(2) model in d = 3, where we predict a large logarithmic correction to the infrared scaling of disorder.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xccxs-hk942N = 4 superconformal bootstrap of the K3 CFT
https://resolver.caltech.edu/CaltechAUTHORS:20170816-083440765
Authors: {'items': [{'id': 'Lin-Ying-Hsuan', 'name': {'family': 'Lin', 'given': 'Ying-Hsuan'}, 'orcid': '0000-0001-8904-1287'}, {'id': 'Shao-Shu-Heng', 'name': {'family': 'Shao', 'given': 'Shu-Heng'}, 'orcid': '0000-0003-1294-2786'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Wang-Yifan', 'name': {'family': 'Wang', 'given': 'Yifan'}, 'orcid': '0000-0001-9965-9777'}, {'id': 'Yin-Xi', 'name': {'family': 'Yin', 'given': 'Xi'}}]}
Year: 2017
DOI: 10.1007/JHEP05(2017)126
We study two-dimensional (4, 4) superconformal field theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS N = 4 superconformal blocks with c = 6 and bosonic Virasoro conformal blocks with c = 28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function. Nontrivial bounds on the non-BPS spectrum in the K3 CFT are obtained as functions of the CFT moduli, that interpolate between the free orbifold points and singular CFT points. We observe directly from the CFT perspective the signature of a continuous spectrum above a gap at the singular moduli, and find numerically an upper bound on this gap that is saturated by the A_1 N = 4 cigar CFT. We also derive an analytic upper bound on the first nonzero eigenvalue of the scalar Laplacian on K3 in the large volume regime, that depends on the K3 moduli data. As two byproducts, we find an exact equivalence between a class of BPS NN = 2 superconformal blocks and Virasoro conformal blocks in two dimensions, and an upper bound on the four-point functions of operators of sufficiently low scaling dimension in three and four dimensional CFTs.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/kbmf6-w4225TASI Lectures on the Conformal Bootstrap
https://resolver.caltech.edu/CaltechAUTHORS:20170817-083513247
Authors: {'items': [{'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2017
DOI: 10.48550/arXiv.1602.07982
These notes are from courses given at TASI and the Advanced Strings School in summer 2015. Starting from principles of quantum field theory and the assumption of a traceless stress tensor, we develop the basics of conformal field theory, including conformal Ward identities, radial quantization, reflection positivity, the operator product expansion, and conformal blocks. We end with an introduction to numerical bootstrap methods, focusing on the 2d and 3d Ising models.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/4z7er-bej14Bootstrapping 3D Fermions with Global Symmetries
https://resolver.caltech.edu/CaltechAUTHORS:20170817-105405345
Authors: {'items': [{'id': 'Iliesiu-Luca', 'name': {'family': 'Iliesiu', 'given': 'Luca'}, 'orcid': '0000-0001-7567-7516'}, {'id': 'Kos-Filip', 'name': {'family': 'Kos', 'given': 'Filip'}, 'orcid': '0000-0001-7332-1655'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Pufu-S-S', 'name': {'family': 'Pufu', 'given': 'Silviu S.'}, 'orcid': '0000-0001-8316-9589'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2018
DOI: 10.1007/JHEP01(2018)036
We study the conformal bootstrap for 4-point functions of fermions 〈ψ_iψ_jψ_kψ_ℓ〉 in parity-preserving 3d CFTs, where ψ_i transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N . For values of N for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y8pg5-dpj18Weight Shifting Operators and Conformal Blocks
https://resolver.caltech.edu/CaltechAUTHORS:20170630-094253636
Authors: {'items': [{'id': 'Karateev-Denis', 'name': {'family': 'Karateev', 'given': 'Denis'}, 'orcid': '0000-0003-4319-9681'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2018
DOI: 10.1007/JHEP02(2018)081
We introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involving operators with spin in conformal field theories. As an application, we derive a formula for a general conformal block (with arbitrary internal and external representations) in terms of derivatives of blocks for external scalars. In particular, our formula gives new expressions for "seed conformal blocks" in 3d and 4d CFTs. We also find simple derivations of identities between external-scalar blocks with different dimensions and internal spins. We comment on additional applications, including deriving recursion relations for general conformal blocks, reducing inversion formulae for spinning operators to inversion formulae for scalars, and deriving identities between general 6j symbols (Racah-Wigner coefficients/"crossing kernels") of the conformal group.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2zvw2-02w77The 3d Stress-Tensor Bootstrap
https://resolver.caltech.edu/CaltechAUTHORS:20170824-150317944
Authors: {'items': [{'id': 'Dymarsky-Anatoly', 'name': {'family': 'Dymarsky', 'given': 'Anatoly'}, 'orcid': '0000-0001-5762-6774'}, {'id': 'Kos-Filip', 'name': {'family': 'Kos', 'given': 'Filip'}, 'orcid': '0000-0001-7332-1655'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2018
DOI: 10.1007/JHEP02(2018)164
We study the conformal bootstrap for 4-point functions of stress tensors in parity-preserving 3d CFTs. To set up the bootstrap equations, we analyze the constraints of conformal symmetry, permutation symmetry, and conservation on the stress-tensor 4-point function and identify a non-redundant set of crossing equations. Studying these equations numerically using semidefinite optimization, we compute bounds on the central charge as a function of the independent coefficient in the stress-tensor 3-point function. With no additional assumptions, these bounds numerically reproduce the conformal collider bounds and give a general lower bound on the central charge. We also study the effect of gaps in the scalar, spin-2, and spin-4 spectra on the central charge bound. We find general upper bounds on these gaps as well as tighter restrictions on the stress-tensor 3-point function coefficients for theories with moderate gaps. When the gap for the leading scalar or spin-2 operator is sufficiently large to exclude large N theories, we also obtain upper bounds on the central charge, thus finding compact allowed regions. Finally, assuming the known low-lying spectrum and central charge of the critical 3d Ising model, we determine its stress-tensor 3-point function and derive a bound on its leading parity-odd scalar.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nthzg-d5210Counting conformal correlators
https://resolver.caltech.edu/CaltechAUTHORS:20180221-104437860
Authors: {'items': [{'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2018
DOI: 10.1007/JHEP02(2018)096
We introduce simple group-theoretic techniques for classifying conformallyinvariant tensor structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and n ≥ 4-point functions of general conserved currents, with or without permutation symmetries, and in any spacetime dimension d. Our techniques are useful for bootstrap applications. The rules we derive simultaneously count tensor structures for flat-space scattering amplitudes in d + 1 dimensions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1dbeh-1c687A spacetime derivation of the Lorentzian OPE inversion formula
https://resolver.caltech.edu/CaltechAUTHORS:20180713-090329998
Authors: {'items': [{'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Stanford-D', 'name': {'family': 'Stanford', 'given': 'Douglas'}}, {'id': 'Witten-E', 'name': {'family': 'Witten', 'given': 'Edward'}, 'orcid': '0000-0002-7752-6073'}]}
Year: 2018
DOI: 10.1007/JHEP07(2018)085
Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian inversion formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y4xtr-qpq55The Conformal Bootstrap at Finite Temperature
https://resolver.caltech.edu/CaltechAUTHORS:20180305-134232971
Authors: {'items': [{'id': 'Iliesiu-Luca', 'name': {'family': 'Iliesiu', 'given': 'Luca'}, 'orcid': '0000-0001-7567-7516'}, {'id': 'Koloğlu-Murat', 'name': {'family': 'Koloğlu', 'given': 'Murat'}, 'orcid': '0000-0002-5082-8434'}, {'id': 'Mahajan-Raghu', 'name': {'family': 'Mahajan', 'given': 'Raghu'}}, {'id': 'Perlmutter-Eric', 'name': {'family': 'Perlmutter', 'given': 'Eric'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2018
DOI: 10.1007/JHEP10(2018)070
We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a "thermal inversion formula" whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O(N) model at leading order in 1/N. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/643k7-9d546Light-ray operators in conformal field theory
https://resolver.caltech.edu/CaltechAUTHORS:20181121-100428583
Authors: {'items': [{'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2018
DOI: 10.1007/JHEP11(2018)102
We argue that every CFT contains light-ray operators labeled by a continuous spin J. When J is a positive integer, light-ray operators become integrals of local operators over a null line. However for non-integer J , light-ray operators are genuinely nonlocal and give the analytic continuation of CFT data in spin described by Caron-Huot. A key role in our construction is played by a novel set of intrinsically Lorentzian integral transforms that generalize the shadow transform. Matrix elements of light-ray operators can be computed via the integral of a double-commutator against a conformal block. This gives a simple derivation of Caron-Huot's Lorentzian OPE inversion formula and lets us generalize it to arbitrary four-point functions. Furthermore, we show that light-ray operators enter the Regge limit of CFT correlators, and generalize conformal Regge theory to arbitrary four-point functions. The average null energy operator is an important example of a light-ray operator. Using our construction, we find a new proof of the average null energy condition (ANEC), and furthermore generalize the ANEC to continuous spin.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pfvvy-rhz66d-dimensional SYK, AdS loops, and 6j symbols
https://resolver.caltech.edu/CaltechAUTHORS:20190314-092752423
Authors: {'items': [{'id': 'Liu-Junyu', 'name': {'family': 'Liu', 'given': 'Junyu'}, 'orcid': '0000-0003-1669-8039'}, {'id': 'Perlmutter-Eric', 'name': {'family': 'Perlmutter', 'given': 'Eric'}}, {'id': 'Rosenhaus-Vladimir', 'name': {'family': 'Rosenhaus', 'given': 'Vladimir'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2019
DOI: 10.1007/jhep03(2019)052
We study the 6j symbol for the conformal group, and its appearance in three seemingly unrelated contexts: the SYK model, conformal representation theory, and perturbative amplitudes in AdS. The contribution of the planar Feynman diagrams to the three-point function of the bilinear singlets in SYK is shown to be a 6j symbol. We generalize the computation of these and other Feynman diagrams to d dimensions. The 6j symbol can be viewed as the crossing kernel for conformal partial waves, which may be computed using the Lorentzian inversion formula. We provide closed-form expressions for 6j symbols in d = 1, 2, 4. In AdS, we show that the 6j symbol is the Lorentzian inversion of a crossing-symmetric tree-level exchange amplitude, thus efficiently packaging the doubletrace OPE data. Finally, we consider one-loop diagrams in AdS with internal scalars and external spinning operators, and show that the triangle diagram is a 6j symbol, while one-loop n-gon diagrams are built out of 6j symbols.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/5gh2a-2aw51Harmonic Analysis and Mean Field Theory
https://resolver.caltech.edu/CaltechAUTHORS:20180917-095421287
Authors: {'items': [{'id': 'Karateev-Denis', 'name': {'family': 'Karateev', 'given': 'Denis'}, 'orcid': '0000-0003-4319-9681'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2019
DOI: 10.1007/JHEP10(2019)217
We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities: one based on weight-shifting operators, and another based on Fourier space. As an application, we give a general formula for OPE coefficients in Mean Field Theory (MFT) for arbitrary spinning operators. We apply this formula to several examples, including MFT for fermions and "seed" operators in 4d, and MFT for currents and stress-tensors in 3d.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0jfjj-0yc18Bootstrapping the 3d Ising model at finite temperature
https://resolver.caltech.edu/CaltechAUTHORS:20181119-150919876
Authors: {'items': [{'id': 'Iliesiu-Luca', 'name': {'family': 'Iliesiu', 'given': 'Luca'}, 'orcid': '0000-0001-7567-7516'}, {'id': 'Koloğlu-Murat', 'name': {'family': 'Koloğlu', 'given': 'Murat'}, 'orcid': '0000-0002-5082-8434'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2019
DOI: 10.1007/JHEP12(2019)072
We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions 〈σσ〉 and 〈ϵϵ〉. As a result, we estimate the one-point functions of the lowest-dimension ℤ₂-even scalar ϵ and the stress energy tensor T_(μν). Our result for 〈σσ〉 at finite-temperature agrees with Monte-Carlo simulations within a few percent, inside the radius of convergence of the OPE.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/1ph1h-6kq67Carving out OPE space and precise O(2) model critical exponents
https://resolver.caltech.edu/CaltechAUTHORS:20200624-104211278
Authors: {'items': [{'id': 'Chester-S-M', 'name': {'family': 'Chester', 'given': 'Shai M.'}}, {'id': 'Landry-Walter', 'name': {'family': 'Landry', 'given': 'Walter'}}, {'id': 'Liu-Junyu', 'name': {'family': 'Liu', 'given': 'Junyu'}, 'orcid': '0000-0003-1669-8039'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Sun-Ning', 'name': {'family': 'Sun', 'given': 'Ning'}}, {'id': 'Vichi-Alessandro', 'name': {'family': 'Vichi', 'given': 'Alessandro'}}]}
Year: 2020
DOI: 10.1007/jhep06(2020)142
We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e8wp0-n1c80The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
https://resolver.caltech.edu/CaltechAUTHORS:20200924-144352084
Authors: {'items': [{'id': 'Liu-Junyu', 'name': {'family': 'Liu', 'given': 'Junyu'}, 'orcid': '0000-0003-1669-8039'}, {'id': 'Meltzer-David', 'name': {'family': 'Meltzer', 'given': 'David'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2020
DOI: 10.1007/jhep09(2020)115
We study the spectrum and OPE coefficients of the three-dimensional critical O(2) model, using four-point functions of the leading scalars with charges 0, 1, and 2 (s, ϕ, and t). We obtain numerical predictions for low-twist OPE data in several charge sectors using the extremal functional method. We compare the results to analytical estimates using the Lorentzian inversion formula and a small amount of numerical input. We find agreement between the analytic and numerical predictions. We also give evidence that certain scalar operators lie on double-twist Regge trajectories and obtain estimates for the leading Regge intercepts of the O(2) model.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b1w6t-09d50Shocks, superconvergence, and a stringy equivalence principle
https://resolver.caltech.edu/CaltechAUTHORS:20190426-081422230
Authors: {'items': [{'id': 'Koloğlu-Murat', 'name': {'family': 'Koloğlu', 'given': 'Murat'}, 'orcid': '0000-0002-5082-8434'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Zhiboedov-Alexander', 'name': {'family': 'Zhiboedov', 'given': 'Alexander'}}]}
Year: 2020
DOI: 10.1007/JHEP11(2020)096
We study propagation of a probe particle through a series of closely situated gravitational shocks. We argue that in any UV-complete theory of gravity the result does not depend on the shock ordering — in other words, coincident gravitational shocks commute. Shock commutativity leads to nontrivial constraints on low-energy effective theories. In particular, it excludes non-minimal gravitational couplings unless extra degrees of freedom are judiciously added. In flat space, these constraints are encoded in the vanishing of a certain "superconvergence sum rule." In AdS, shock commutativity becomes the statement that average null energy (ANEC) operators commute in the dual CFT. We prove commutativity of ANEC operators in any unitary CFT and establish sufficient conditions for commutativity of more general light-ray operators. Superconvergence sum rules on CFT data can be obtained by inserting complete sets of states between light-ray operators. In a planar 4d CFT, these sum rules express a−c/c in terms of the OPE data of single-trace operators.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/y0b3q-ykj66Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs
https://resolver.caltech.edu/CaltechAUTHORS:20201113-100153642
Authors: {'items': [{'id': 'Fitzpatrick-A-L', 'name': {'family': 'Fitzpatrick', 'given': 'A. Liam'}}, {'id': 'Huang-Kuo-Wei', 'name': {'family': 'Huang', 'given': 'Kuo-Wei'}}, {'id': 'Meltzer-David', 'name': {'family': 'Meltzer', 'given': 'David'}}, {'id': 'Perlmutter-Eric', 'name': {'family': 'Perlmutter', 'given': 'Eric'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2020
DOI: 10.1007/jhep11(2020)060
Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge CT, we clarify the properties of stress tensor composite primary operators of minimal twist, [Tᵐ], using arguments in both CFT and gravity. We provide an efficient proof that the three-point coupling 〈O_LO_L[Tᵐ]〉, where O_L is any light primary operator, is independent of the purely gravitational action. Next, we consider corrections to this coupling due to additional interactions in AdS effective field theory and the corresponding dual CFT. When the CFT contains a non-zero three-point coupling 〈TTO_L 〉, the three-point coupling 〈O_LO_L[T²]〉 is modified at large C_T if 〈TTO_L 〉 ~ √C_T. This scaling is obeyed by the dilaton, by Kaluza-Klein modes of prototypical supergravity compactifications, and by scalars in stress tensor multiplets of supersymmetric CFTs. Quartic derivative interactions involving the graviton and the light probe field dual to O_L can also modify the minimal-twist couplings; these local interactions may be generated by integrating out a spin-ℓ ≥ 2 bulk field at tree level, or any spin ℓ at loop level. These results show how the minimal-twist OPE coefficients can depend on the higher-spin gap scale, even perturbatively.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/e5fsq-2ya41Scaling the semidefinite program solver SDPB
https://resolver.caltech.edu/CaltechAUTHORS:20201118-081637808
Authors: {'items': [{'id': 'Landry-Walter', 'name': {'family': 'Landry', 'given': 'Walter'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2020
DOI: 10.48550/arXiv.1909.09745
We present enhancements to SDPB, an open source, parallelized, arbitrary precision semidefinite program solver designed for the conformal bootstrap. The main enhancement is significantly improved performance and scalability using the Elemental library and MPI. The result is a new version of SDPB that runs on multiple nodes with hundreds of cores with excellent scaling, making it practical to solve larger problems. We demonstrate performance on a moderate-size problem in the 3d Ising CFT and a much larger problem in the O(2) Model.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6m6v7-6f391The light-ray OPE and conformal colliders
https://resolver.caltech.edu/CaltechAUTHORS:20190709-151426552
Authors: {'items': [{'id': 'Koloğlu-Murat', 'name': {'family': 'Koloğlu', 'given': 'Murat'}, 'orcid': '0000-0002-5082-8434'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Zhiboedov-Alexander', 'name': {'family': 'Zhiboedov', 'given': 'Alexander'}}]}
Year: 2021
DOI: 10.1007/JHEP01(2021)128
We derive a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. The objects appearing in the expansion are light-ray operators, whose matrix elements can be computed by the generalized Lorentzian inversion formula. For example, a product of average null energy (ANEC) operators has an expansion in the light-ray operators that appear in the stress-tensor OPE. An important application is to collider event shapes. The light-ray OPE gives a nonperturbative expansion for event shapes in special functions that we call celestial blocks. As an example, we apply the celestial block expansion to energy-energy correlators in N = 4 Super Yang-Mills theory. Using known OPE data, we find perfect agreement with previous results both at weak and strong coupling, and make new predictions at weak coupling through 4 loops (NNNLO).https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/epxdw-s1053Dispersive CFT sum rules
https://resolver.caltech.edu/CaltechAUTHORS:20201118-074154634
Authors: {'items': [{'id': 'Caron-Huot-Simon', 'name': {'family': 'Caron-Huot', 'given': 'Simon'}}, {'id': 'Mazáč-Dalimil', 'name': {'family': 'Mazáč', 'given': 'Dalimil'}}, {'id': 'Rastelli-Leonardo', 'name': {'family': 'Rastelli', 'given': 'Leonardo'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2021
DOI: 10.1007/JHEP05(2021)243
We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory. We call a sum rule "dispersive" if it has double zeros at all double-twist operators above a fixed twist gap. Dispersive sum rules have their conceptual origin in Lorentzian kinematics and absorptive physics (the notion of double discontinuity). They have been discussed using three seemingly different methods: analytic functionals dual to double-twist operators, dispersion relations in position space, and dispersion relations in Mellin space. We show that these three approaches can be mapped into one another and lead to completely equivalent sum rules. A central idea of our discussion is a fully nonperturbative expansion of the correlator as a sum over Polyakov-Regge blocks. Unlike the usual OPE sum, the Polyakov-Regge expansion utilizes the data of two separate channels, while having (term by term) good Regge behavior in the third channel. We construct sum rules which are non-negative above the double-twist gap; they have the physical interpretation of a subtracted version of "superconvergence" sum rules. We expect dispersive sum rules to be a very useful tool to study expansions around mean-field theory, and to constrain the low-energy description of holographic CFTs with a large gap. We give examples of the first kind of applications, notably we exhibit a candidate extremal functional for the spin-two gap problem.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pgtg6-e2n13Sharp boundaries for the swampland
https://resolver.caltech.edu/CaltechAUTHORS:20210730-161344799
Authors: {'items': [{'id': 'Caron-Huot-Simon', 'name': {'family': 'Caron-Huot', 'given': 'Simon'}}, {'id': 'Mazáč-Dalimil', 'name': {'family': 'Mazáč', 'given': 'Dalimil'}, 'orcid': '0000-0003-2613-0906'}, {'id': 'Rastelli-Leonardo', 'name': {'family': 'Rastelli', 'given': 'Leonardo'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2021
DOI: 10.1007/jhep07(2021)110
We reconsider the problem of bounding higher derivative couplings in consistent weakly coupled gravitational theories, starting from general assumptions about analyticity and Regge growth of the S-matrix. Higher derivative couplings are expected to be of order one in the units of the UV cutoff. Our approach justifies this expectation and allows to prove precise bounds on the order one coefficients. Our main tool are dispersive sum rules for the S-matrix. We overcome the difficulties presented by the graviton pole by measuring couplings at small impact parameter, rather than in the forward limit. We illustrate the method in theories containing a massless scalar coupled to gravity, and in theories with maximal supersymmetry.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c7qkk-qht37Navigator function for the conformal bootstrap
https://resolver.caltech.edu/CaltechAUTHORS:20211117-173310983
Authors: {'items': [{'id': 'Reehorst-Marten', 'name': {'family': 'Reehorst', 'given': 'Marten'}}, {'id': 'Rychkov-Slava', 'name': {'family': 'Rychkov', 'given': 'Slava'}, 'orcid': '0000-0002-5847-1011'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Sirois-Benoit', 'name': {'family': 'Sirois', 'given': 'Benoit'}, 'orcid': '0000-0003-3260-4135'}, {'id': 'Su-Ning', 'name': {'family': 'Su', 'given': 'Ning'}, 'orcid': '0000-0001-5559-7922'}, {'id': 'van-Rees-Balt', 'name': {'family': 'van Rees', 'given': 'Balt'}, 'orcid': '0000-0003-0904-5881'}]}
Year: 2021
DOI: 10.21468/scipostphys.11.3.072
Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are well-defined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hd2y7-epd41blocks_3d: software for general 3d conformal blocks
https://resolver.caltech.edu/CaltechAUTHORS:20201111-132131256
Authors: {'items': [{'id': 'Erramilli-Rajeev-S', 'name': {'family': 'Erramilli', 'given': 'Rajeev S.'}}, {'id': 'Iliesiu-Luca', 'name': {'family': 'Iliesiu', 'given': 'Luca V.'}, 'orcid': '0000-0001-7567-7516'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Landry-Walter', 'name': {'family': 'Landry', 'given': 'Walter'}}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2021
DOI: 10.1007/JHEP11(2021)006
We introduce the software blocks_3d for computing four-point conformal blocks of operators with arbitrary Lorentz representations in 3d CFTs. It uses Zamolodchikov-like recursion relations to numerically compute derivatives of blocks around a crossing-symmetric configuration. It is implemented as a heavily optimized, multi-threaded, C++ application. We give performance benchmarks for correlators containing scalars, fermions, and stress tensors. As an example application, we recompute bootstrap bounds on four-point functions of fermions and study whether a previously observed sharp jump can be explained using the "fake primary" effect. We conclude that the fake primary effect cannot fully explain the jump and the possible existence of a "dead-end" CFT near the jump merits further study.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/x5r40-fc154AdS bulk locality from sharp CFT bounds
https://resolver.caltech.edu/CaltechAUTHORS:20211207-6309000
Authors: {'items': [{'id': 'Caron-Huot-Simon', 'name': {'family': 'Caron-Huot', 'given': 'Simon'}}, {'id': 'Mazáč-Dalimil', 'name': {'family': 'Mazáč', 'given': 'Dalimil'}, 'orcid': '0000-0003-2613-0906'}, {'id': 'Rastelli-Leonardo', 'name': {'family': 'Rastelli', 'given': 'Leonardo'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2021
DOI: 10.1007/jhep11(2021)164
It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆gap in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆_(gap) using the conformal bootstrap. Our bounds exhibit the scaling in ∆_(gap) expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS₄ naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8a8aq-9jy19Bootstrapping Heisenberg magnets and their cubic instability
https://resolver.caltech.edu/CaltechAUTHORS:20201203-155726059
Authors: {'items': [{'id': 'Chester-Shai-M', 'name': {'family': 'Chester', 'given': 'Shai M.'}, 'orcid': '0000-0001-8803-1511'}, {'id': 'Landry-Walter', 'name': {'family': 'Landry', 'given': 'Walter'}}, {'id': 'Liu-Junyu', 'name': {'family': 'Liu', 'given': 'Junyu'}, 'orcid': '0000-0003-1669-8039'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Su-Ning', 'name': {'family': 'Su', 'given': 'Ning'}, 'orcid': '0000-0001-5559-7922'}, {'id': 'Vichi-Alessandro', 'name': {'family': 'Vichi', 'given': 'Alessandro'}, 'orcid': '0000-0001-6577-6887'}]}
Year: 2021
DOI: 10.1103/PhysRevD.104.105013
We study the critical O(3) model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of conformal field theory data from correlators involving the leading O(3) singlet s, vector ϕ, and rank-2 symmetric tensor t. We determine their scaling dimensions to be (Δ_ϕ,Δ_s,Δ_t) = (0.518942(51), 1.59489(59), 1.20954(23)), and also bound various operator product expansion coefficients. We additionally introduce a new "tip-finding" algorithm to compute an upper bound on the leading rank-4 symmetric tensor t₄, which we find to be relevant with Δt₄ < 2.99056. The conformal bootstrap thus provides a numerical proof that systems described by the critical O(3) model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fgxks-e5e20Transverse spin in the light-ray OPE
https://resolver.caltech.edu/CaltechAUTHORS:20201013-113712492
Authors: {'items': [{'id': 'Chang-Cyuan-Han', 'name': {'family': 'Chang', 'given': 'Cyuan-Han'}, 'orcid': '0000-0002-7133-3553'}, {'id': 'Koloğlu-Murat', 'name': {'family': 'Koloğlu', 'given': 'Murat'}, 'orcid': '0000-0002-5082-8434'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Zhiboedov-Alexander', 'name': {'family': 'Zhiboedov', 'given': 'Alexander'}, 'orcid': '0000-0002-7065-1904'}]}
Year: 2022
DOI: 10.1007/JHEP05(2022)059
We study a product of null-integrated local operators O₁ and O₂ on the same null plane in a CFT. Such null-integrated operators transform like primaries in a fictitious d − 2 dimensional CFT in the directions transverse to the null integrals. We give a complete description of the OPE in these transverse directions. The terms with low transverse spin are light-ray operators with spin J₁ + J₂ − 1. The terms with higher transverse spin are primary descendants of light-ray operators with higher spins J₁ + J₂ − 1 + n, constructed using special conformally-invariant differential operators that appear precisely in the kinematics of the light-ray OPE. As an example, the OPE between average null energy operators contains light-ray operators with spin 3 (as described by Hofman and Maldacena), but also novel terms with spin 5, 7, 9, etc. These new terms are important for describing energy two-point correlators in non-rotationally-symmetric states, and for computing multi-point energy correlators. We check our formulas in a non-rotationally-symmetric energy correlator in N = 4 SYM, finding perfect agreement.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/30c1b-mz061Fast Arbitrary Precision Floating Point on FPGA
https://resolver.caltech.edu/CaltechAUTHORS:20220614-222241000
Authors: {'items': [{'id': 'de-Fine-Licht-Johannes', 'name': {'family': 'de Fine Licht', 'given': 'Johannes'}, 'orcid': '0000-0002-1500-7411'}, {'id': 'Pattison-Christopher-A', 'name': {'family': 'Pattison', 'given': 'Christopher A.'}}, {'id': 'Ziogas-Alexandros-Nikolaos', 'name': {'family': 'Ziogas', 'given': 'Alexandros Nikolaos'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}, {'id': 'Hoefler-Torsten', 'name': {'family': 'Hoefler', 'given': 'Torsten'}, 'orcid': '0000-0001-9611-7171'}]}
Year: 2022
DOI: 10.1109/fccm53951.2022.9786219
Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits. APFP computations on conventional software-based architectures are made exceedingly expensive by the lack of native hardware support, requiring elementary operations to be emulated using instructions operating on machine-word-sized blocks. In this work, we show how APFP multiplication on compile-time fixed-precision operands can be implemented as deep FPGA pipelines with a recursively defined Karatsuba decomposition on top of native DSP multiplication. When comparing our design implemented on an Alveo U250 accelerator to a dual-socket 36-core Xeon node running the GNU Multiple Precision Floating-Point Reliable (MPFR) library, we achieve a 9.8× speedup at 4.8 GOp/s for 512-bit multiplication, and a 5.3× speedup at 1.2 GOp/s for 1024-bit multiplication, corresponding to the throughput of more than 351× and 191× CPU cores, respectively. We apply this architecture to general matrix-matrix multiplication, yielding a 10× speedup at 2.0 GOp/s over the Xeon node, equivalent to more than 375× CPU cores, effectively allowing a single FPGA to replace a small CPU cluster. Due to the significant dependence of some numerical codes on APFP, such as semidefinite program solvers, we expect these gains to translate into real-world speedups. Our configurable and flexible HLS-based code provides as high-level software interface for plug-and-play acceleration, published as an open source project.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9vcnc-sx057Detectors in weakly-coupled field theories
https://resolver.caltech.edu/CaltechAUTHORS:20220922-222020207
Authors: {'items': [{'id': 'Caron-Huot-Simon', 'name': {'family': 'Caron-Huot', 'given': 'Simon'}}, {'id': 'Koloğlu-Murat', 'name': {'family': 'Koloğlu', 'given': 'Murat'}, 'orcid': '0000-0002-5082-8434'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Meltzer-David', 'name': {'family': 'Meltzer', 'given': 'David'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2022
DOI: 10.48550/arXiv.2209.00008
We initiate a study of asymptotic detector operators in weakly-coupled field theories. These operators describe measurements that can be performed at future null infinity in a collider experiment. In a conformal theory they can be identified with light-ray operators, and thus have a direct relation to the spectrum of the theory. After a general discussion of the underlying physical picture, we show how infrared divergences of general detector operators can be renormalized in perturbation theory, and how they give rise to detector anomalous dimensions. We discuss in detail how this renormalization can be performed at the intersections of the Regge trajectories where non-trivial mixing occurs, which is related to the poles in anomalous dimensions at special values of spin. Finally, we discuss novel horizontal trajectories in scalar theories and show how they contribute to correlation functions. Our calculations are done in the example of ϕ⁴ theory in d = 4 − ϵ dimensions, but the methods are applicable more broadly. At the Wilson-Fisher fixed point our results include an explicit expression for the Pomeron light-ray operator at two loops, as well as a prediction for the value of the Regge intercept at five loops.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hh7j4-1x426The Gross-Neveu-Yukawa archipelago
https://resolver.caltech.edu/CaltechAUTHORS:20230307-205876300.25
Authors: {'items': [{'id': 'Erramilli-Rajeev-S', 'name': {'family': 'Erramilli', 'given': 'Rajeev S.'}, 'orcid': '0000-0001-9854-5196'}, {'id': 'Iliesiu-Luca', 'name': {'family': 'Iliesiu', 'given': 'Luca V.'}, 'orcid': '0000-0001-7567-7516'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Liu-Aike', 'name': {'family': 'Liu', 'given': 'Aike'}, 'orcid': '0009-0009-8509-4635'}, {'id': 'Poland-David', 'name': {'family': 'Poland', 'given': 'David'}, 'orcid': '0000-0003-3854-2430'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2023
DOI: 10.1007/jhep02(2023)036
We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/0mrva-f0930Detectors in weakly-coupled field theories
https://resolver.caltech.edu/CaltechAUTHORS:20230502-485091700.4
Authors: {'items': [{'id': 'Caron-Huot-Simon', 'name': {'family': 'Caron-Huot', 'given': 'Simon'}}, {'id': 'Koloğlu-Murat', 'name': {'family': 'Koloğlu', 'given': 'Murat'}, 'orcid': '0000-0002-5082-8434'}, {'id': 'Kravchuk-Petr', 'name': {'family': 'Kravchuk', 'given': 'Petr'}, 'orcid': '0000-0003-0977-3686'}, {'id': 'Meltzer-David', 'name': {'family': 'Meltzer', 'given': 'David'}}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2023
DOI: 10.1007/jhep04(2023)014
We initiate a study of asymptotic detector operators in weakly-coupled field theories. These operators describe measurements that can be performed at future null infinity in a collider experiment. In a conformal theory they can be identified with light-ray operators, and thus have a direct relation to the spectrum of the theory. After a general discussion of the underlying physical picture, we show how infrared divergences of general detector operators can be renormalized in perturbation theory, and how they give rise to detector anomalous dimensions. We discuss in detail how this renormalization can be performed at the intersections of the Regge trajectories where non-trivial mixing occurs, which is related to the poles in anomalous dimensions at special values of spin. Finally, we discuss novel horizontal trajectories in scalar theories and show how they contribute to correlation functions. Our calculations are done in the example of ϕ⁴ theory in d = 4 − ϵ dimensions, but the methods are applicable more broadly. At the Wilson-Fisher fixed point our results include an explicit expression for the Pomeron light-ray operator at two loops, as well as a prediction for the value of the Regge intercept at five loops.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tyq08-12627Causality constraints on corrections to Einstein gravity
https://resolver.caltech.edu/CaltechAUTHORS:20230530-441187700.14
Authors: {'items': [{'id': 'Caron-Huot-Simon', 'name': {'family': 'Caron-Huot', 'given': 'Simon'}, 'orcid': '0000-0002-7005-9652'}, {'id': 'Li-Yue-Zhou', 'name': {'family': 'Li', 'given': 'Yue-Zhou'}, 'orcid': '0000-0002-3982-4838'}, {'id': 'Parra-Martinez-Julio', 'name': {'family': 'Parra-Martinez', 'given': 'Julio'}, 'orcid': '0000-0003-0178-1569'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2023
DOI: 10.1007/jhep05(2023)122
We study constraints from causality and unitarity on 2 → 2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G → 0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/g438j-zye19Graviton partial waves and causality in higher dimensions
https://authors.library.caltech.edu/records/02gzj-9pd02
Authors: {'items': [{'id': 'Caron-Huot-Simon', 'name': {'family': 'Caron-Huot', 'given': 'Simon'}, 'orcid': '0000-0002-7005-9652'}, {'id': 'Li-Yue-Zhou', 'name': {'family': 'Li', 'given': 'Yue-Zhou'}, 'orcid': '0000-0002-3982-4838'}, {'id': 'Parra-Martinez-Julio', 'name': {'family': 'Parra-Martinez', 'given': 'Julio'}, 'orcid': '0000-0003-0178-1569'}, {'id': 'Simmons-Duffin-D', 'name': {'family': 'Simmons-Duffin', 'given': 'David'}, 'orcid': '0000-0002-2937-9515'}]}
Year: 2023
DOI: 10.1103/physrevd.108.026007
<p>Do gravitational interactions respect the basic principles of relativity and quantum mechanics? We show that any graviton <i>S</i>-matrix that satisfies these assumptions cannot significantly differ from General Relativity at low energies. We provide sharp bounds on the size of potential corrections in terms of the mass <i>M</i> of new higher-spin states, in spacetime dimensions <i>D</i> ≥ 5 where the S-matrix does not suffer from infrared ambiguities. The key novel ingredient is the full set of <i>SO</i>(<i>D</i> − 1) partial waves for this process, which we show how to efficiently compute with Young tableau manipulations. We record new bounds on the central charges of holographic conformal theories.</p>https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/02gzj-9pd02