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https://feeds.library.caltech.edu/people/Trnka-J/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:24:31 +0000The Amplituhedron
https://resolver.caltech.edu/CaltechAUTHORS:20141120-102508525
Authors: {'items': [{'id': 'Arkani-Hamed-N', 'name': {'family': 'Arkani-Hamed', 'given': 'Nima'}}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2014
DOI: 10.1007/JHEP10(2014)030
Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for N=4 SYM scattering amplitudes in the planar limit, which we identify as "the volume" of a new mathematical object — the Amplituhedron — generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.https://authors.library.caltech.edu/records/7gpyv-f1276Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
https://resolver.caltech.edu/CaltechAUTHORS:20141216-210539178
Authors: {'items': [{'id': 'Arkani-Hamed-N', 'name': {'family': 'Arkani-Hamed', 'given': 'Nima'}}, {'id': 'Bourjaily-J-L', 'name': {'family': 'Bourjaily', 'given': 'Jacob L.'}}, {'id': 'Cachazo-Freddy', 'name': {'family': 'Cachazo', 'given': 'Freddy'}}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2014
DOI: 10.1103/PhysRevLett.113.261603
We present evidence that loop amplitudes in maximally supersymmetric (N=4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N=4 SYM has only logarithmic singularities and is free of any poles at infinity—properties closely related to uniform transcendentality and the UV finiteness of the theory. We also briefly comment on implications for maximal (N=8) supergravity theory (SUGRA).https://authors.library.caltech.edu/records/0sy20-5zf47Into the amplituhedron
https://resolver.caltech.edu/CaltechAUTHORS:20150202-084533756
Authors: {'items': [{'id': 'Arkani-Hamed-N', 'name': {'family': 'Arkani-Hamed', 'given': 'Nima'}}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2014
DOI: 10.1007/JHEP12(2014)182
We initiate an exploration of the physics and geometry of the amplituhedron, starting with the simplest case of the integrand for four-particle scattering in planar N=4 SYM. We show how the textbook structure of the unitarity double-cut follows from the positive geometry. We also use the geometry to expose the behavior of the multicollinear limit, providing a direct motivation for studying the logarithm of the amplitude. In addition to computing the two and three-loop integrands, we explore various lower-dimensional faces of the amplituhedron, thereby computing non-trivial cuts of the integrand to all loop orders.https://authors.library.caltech.edu/records/01za7-5wm26On-Shell Structures of MHV Amplitudes Beyond the Planar Limit
https://resolver.caltech.edu/CaltechAUTHORS:20150122-082315937
Authors: {'items': [{'id': 'Arkani-Hamed-N', 'name': {'family': 'Arkani-Hamed', 'given': 'Nima'}}, {'id': 'Bourjaily-J-L', 'name': {'family': 'Bourjaily', 'given': 'Jacob L.'}}, {'id': 'Cachazo-Freddy', 'name': {'family': 'Cachazo', 'given': 'Freddy'}}, {'id': 'Postnikov-Alexander', 'name': {'family': 'Postnikov', 'given': 'Alexander'}}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2015
DOI: 10.1007/JHEP06(2015)179
We initiate an exploration of on-shell functions in N = 4 SYM beyond the planar limit by providing compact, combinatorial expressions for all leading singularities of MHV amplitudes and showing that they can always be expressed as a positive sum of differently ordered Parke-Taylor tree amplitudes. This is understood in terms of an extended notion of positivity in G(2, n), the Grassmannian of 2-planes in n dimensions: a single on-shell diagram can be associated with many different "positive" regions, of which the familiar G_+(2, n) associated with planar diagrams is just one example. The decomposition into Parke-Taylor factors is simply a "triangulation" of these extended positive regions. The U(1) decoupling and Kleiss-Kuijf (KK) relations satisfied by the Parke-Taylor amplitudes also follow naturally from this geometric picture. These results suggest that non-planar MHV amplitudes in N = 4 SYM at all loop orders can be expressed as a sum of polylogarithms weighted by color factors and (unordered) Parke-Taylor amplitudes.https://authors.library.caltech.edu/records/8f9d9-58x40Effective Field Theories from Soft Limits of Scattering Amplitudes
https://resolver.caltech.edu/CaltechAUTHORS:20141216-134735706
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Kampk-K', 'name': {'family': 'Kampf', 'given': 'Karol'}, 'orcid': '0000-0003-1096-667X'}, {'id': 'Novotny-J', 'name': {'family': 'Novotny', 'given': 'Jiri'}}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2015
DOI: 10.1103/PhysRevLett.114.221602
We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.https://authors.library.caltech.edu/records/731b6-xq145Simple Recursion Relations for General Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20150311-194335939
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2015
DOI: 10.1007/JHEP06(2015)118
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.https://authors.library.caltech.edu/records/c075k-m0j21Positive Amplitudes In The Amplituhedron
https://resolver.caltech.edu/CaltechAUTHORS:20150316-142202703
Authors: {'items': [{'id': 'Arkani-Hamed-N', 'name': {'family': 'Arkani-Hamed', 'given': 'Nima'}}, {'id': 'Hodges-A', 'name': {'family': 'Hodges', 'given': 'Andrew'}}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2015
DOI: 10.1007/JHEP08(2015)030
The all-loop integrand for scattering amplitudes in planar N = 4 SYM is determined by an "amplitude form" with logarithmic singularities on the boundary of the amplituhedron. In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron. The statement is sensibly formulated thanks to the natural "bosonization" of the superamplitude associated with the amplituhedron geometry. However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian. The surprising positivity of the form suggests the existence of a "dual amplituhedron" formulation where this feature would be made obvious. We also suggest that the positivity is associated with an extended picture of amplituhedron geometry, with the amplituhedron sitting inside a co-dimension one surface separating "legal" and "illegal" local singularities of the amplitude. We illustrate this in several simple examples, obtaining new expressions for amplitudes not associated with any triangulations, but following in a more invariant manner from a global view of the positive geometry.https://authors.library.caltech.edu/records/2qmz0-heq72Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
https://resolver.caltech.edu/CaltechAUTHORS:20150814-090422946
Authors: {'items': [{'id': 'Bourjaily-J-L', 'name': {'family': 'Bourjaily', 'given': 'Jacob L.'}}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2015
DOI: 10.1007/JHEP08(2015)119
We use generalized unitarity at the integrand-level to directly construct
local, manifestly dual-conformally invariant formulae for all two-loop
scattering amplitudes in planar, maximally supersymmetric Yang-Mills theory
(SYM). This representation separates contributions into manifestly finite and
manifestly divergent terms---in a way that renders all infrared-safe
observables (including ratio functions) calculable without any need for
regulation. These results perfectly match the all-loop BCFW recursion
relations, to which we provide a closed-form solution valid through
two-loop-order. Finally, we describe and document a Mathematica package which
implements these results, available as part of this work's source files on the
arXiv.https://authors.library.caltech.edu/records/mapp0-4tn80On-Shell Recursion Relations for Effective Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20151022-121225042
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Kampf-K', 'name': {'family': 'Kampf', 'given': 'Karol'}}, {'id': 'Novotny-J', 'name': {'family': 'Novotny', 'given': 'Jiri'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2016
DOI: 10.1103/PhysRevLett.116.041601
We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.https://authors.library.caltech.edu/records/2r60g-92j88A Periodic Table of Effective Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20161114-161621602
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Kampk-K', 'name': {'family': 'Kampf', 'given': 'Karol'}, 'orcid': '0000-0003-1096-667X'}, {'id': 'Novotny-J', 'name': {'family': 'Novotny', 'given': 'Jiri'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}]}
Year: 2017
DOI: 10.1007/JHEP02(2017)020
We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.https://authors.library.caltech.edu/records/t2kee-x9e40Vector Effective Field Theories from Soft Limits
https://resolver.caltech.edu/CaltechAUTHORS:20180117-160027517
Authors: {'items': [{'id': 'Cheung-Clifford', 'name': {'family': 'Cheung', 'given': 'Clifford'}, 'orcid': '0000-0002-9983-9425'}, {'id': 'Kampk-K', 'name': {'family': 'Kampf', 'given': 'Karol'}, 'orcid': '0000-0003-1096-667X'}, {'id': 'Novotny-J', 'name': {'family': 'Novotny', 'given': 'Jiri'}}, {'id': 'Shen-Chia-Hsien', 'name': {'family': 'Shen', 'given': 'Chia-Hsien'}, 'orcid': '0000-0002-5138-9971'}, {'id': 'Trnka-J', 'name': {'family': 'Trnka', 'given': 'Jaroslav'}}, {'id': 'Wen-Congkao', 'name': {'family': 'Wen', 'given': 'Congkao'}, 'orcid': '0000-0002-5174-1576'}]}
Year: 2018
DOI: 10.1103/PhysRevLett.120.261602
We present a bottom-up construction of vector effective field theories using the infrared structure of scattering amplitudes. Our results employ two distinct probes of soft kinematics: multiple soft limits and single soft limits after dimensional reduction applicable in four and general dimensions, respectively. Both approaches uniquely specify the Born-Infeld (BI) model as the only theory of vectors completely fixed by certain infrared conditions which generalize the Adler zero for pions. These soft properties imply new recursion relations for on-shell scattering amplitudes in BI theory and suggest the existence of a wider class of vector effective field theories.https://authors.library.caltech.edu/records/h883z-s7g63