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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 01:44:44 +0000The Verlinde formula for Higgs bundles
https://resolver.caltech.edu/CaltechAUTHORS:20160816-123626732
Authors: {'items': [{'id': 'Andersen-J-E', 'name': {'family': 'Andersen', 'given': 'Jørgen Ellegaard'}, 'orcid': '0000-0001-9721-0722'}, {'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}]}
Year: 2016
DOI: 10.48550/arXiv.1608.01761
We propose and prove the Verlinde formula for the quantization of the Higgs
bundle moduli spaces and stacks for any simple and simply-connected group. This
generalizes the equivariant Verlinde formula for the case of SU(n) proposed
previously by the second and third author. We further establish a Verlinde
formula for the quantization of parabolic Higgs bundle moduli spaces and
stacks.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9deyp-p1157A 3d-3d appetizer
https://resolver.caltech.edu/CaltechAUTHORS:20150324-090428497
Authors: {'items': [{'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Ye-Ke', 'name': {'family': 'Ye', 'given': 'Ke'}, 'orcid': '0000-0002-2978-2013'}]}
Year: 2016
DOI: 10.1007/JHEP11(2016)008
We test the 3d-3d correspondence for theories that are labeled by Lens spaces. We find a full agreement between the index of the 3d N=2 "Lens space theory" T [L(p, 1)] and the partition function of complex Chern-Simons theory on L(p, 1). In particular, for p = 1, we show how the familiar S^3 partition function of Chern-Simons theory arises from the index of a free theory. For large p, we find that the index of T[L(p, 1)] becomes a constant independent of p. In addition, we study T[L(p, 1)] on the squashed three-sphere S_b^3. This enables us to see clearly, at the level of partition function, to what extent Gℂ complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group G.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/9k6mj-e9298Equivariant Verlinde formula from fivebranes and vortices
https://resolver.caltech.edu/CaltechAUTHORS:20150220-093858198
Authors: {'items': [{'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}]}
Year: 2017
DOI: 10.1007/s00220-017-2931-9
We study complex Chern–Simons theory on a Seifert manifold M_3 by embedding it into string theory. We show that complex Chern–Simons theory on M_3 is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern–Simons theory on Σ×S^1 and (4) index of a spin^c Dirac operator on the moduli space of flat connections to a new set of relations between (1) the "equivariant Verlinde algebra" for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern–Simons theory on Σ×S^1 and (4) the equivariant index of a spin^c Dirac operator on the moduli space of Higgs bundles.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7kxbt-v6s41Mirror symmetry with branes by equivariant Verlinde formulae
https://resolver.caltech.edu/CaltechAUTHORS:20171214-111513089
Authors: {'items': [{'id': 'Hausel-T', 'name': {'family': 'Hausel', 'given': 'Tamas'}}, {'id': 'Mellit-A', 'name': {'family': 'Mellit', 'given': 'Anton'}}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}]}
Year: 2017
DOI: 10.48550/arXiv.1712.04408
We find an agreement of equivariant indices of semi-classical homomorphisms
between pairwise mirror branes in the GL(2) Higgs moduli space on a Riemann
surface. On one side we have the components of the Lagrangian brane of U(1,1)
Higgs bundles whose mirror was proposed by Nigel Hitchin to be certain even
exterior powers of the hyperholomorphic Dirac bundle on the SL(2) Higgs moduli
space. The agreement arises from a mysterious functional equation. This gives
strong computational evidence for Hitchin's proposal.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bsm0r-b9z58Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
https://resolver.caltech.edu/CaltechAUTHORS:20160707-133458529
Authors: {'items': [{'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Yan-Wenbin', 'name': {'family': 'Yan', 'given': 'Wenbin'}}, {'id': 'Ye-Ke', 'name': {'family': 'Ye', 'given': 'Ke'}, 'orcid': '0000-0002-2978-2013'}]}
Year: 2018
DOI: 10.1007/s00220-017-3074-8
In this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the "Coulomb branch index" of the class SS theory T[Σ,G] on L(k,1)×S^1, the other is the LGLG "equivariant Verlinde formula", or equivalently partition function of LGCLGC complex Chern–Simons theory on Σ×S^1. We first derive this equivalence using the M-theory geometry and show that the gauge groups appearing on the two sides are naturally G and its Langlands dual LGLG. When G is not simply-connected, we provide a recipe of computing the index of T[Σ,G] as summation over the indices of T[Σ,G] with non-trivial background 't Hooft fluxes, where G is the universal cover of G. Then we check explicitly this relation between the Coulomb index and the equivariant Verlinde formula for G=SU(2) or SO(3). In the end, as an application of this newly found relation, we consider the more general case where G is SU(N) or PSU(N) and show that equivariant Verlinde algebra can be derived using field theory via (generalized) Argyres–Seiberg duality. We also attach a Mathematica notebook that can be used to compute the SU(3) equivariant Verlinde coefficients.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ywftn-q2j47Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
https://resolver.caltech.edu/CaltechAUTHORS:20170201-094330289
Authors: {'items': [{'id': 'Fredrickson-L', 'name': {'family': 'Fredrickson', 'given': 'Laura'}}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Yan-Wenbin', 'name': {'family': 'Yan', 'given': 'Wenbin'}}, {'id': 'Ye-Ke', 'name': {'family': 'Ye', 'given': 'Ke'}, 'orcid': '0000-0002-2978-2013'}]}
Year: 2018
DOI: 10.1007/JHEP01(2018)150
We use Coulomb branch indices of Argyres-Douglas theories on S1×L(k,1) to quantize moduli spaces M_H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" -- the graded dimensions of the Hilbert spaces from quantization -- for four infinite families of M_H, giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in M_H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform STkS in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/q4ma4-w1932Identities for Poincaré polynomials via Kostant cascades
https://resolver.caltech.edu/CaltechAUTHORS:20181026-105826496
Authors: {'items': [{'id': 'Andersen-J-E', 'name': {'family': 'Andersen', 'given': 'Jørgen Ellegaard'}, 'orcid': '0000-0001-9721-0722'}, {'id': 'Jantzen-J-C', 'name': {'family': 'Jantzen', 'given': 'Jens Carsten'}}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}]}
Year: 2018
DOI: 10.48550/arXiv.1810.05615
We propose and prove an identity relating the Poincar\'e polynomials of
stabilizer subgroups of the affine Weyl group and of the corresponding
stabilizer subgroups of the Weyl group.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/nfn7a-jad05BPS spectra and 3-manifold invariants
https://resolver.caltech.edu/CaltechAUTHORS:20170201-100930550
Authors: {'items': [{'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Putrov-P', 'name': {'family': 'Putrov', 'given': 'Pavel'}}, {'id': 'Vafa-C', 'name': {'family': 'Vafa', 'given': 'Cumrun'}}]}
Year: 2020
DOI: 10.1142/S0218216520400039
We provide a physical definition of new homological invariants H_a(M₃) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M₃ times a 2-disk, D², whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d N=2 theory T[M₃]: D²×S¹ half-index, S²×S¹ superconformal index, and S²×S¹ topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern–Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of M₃. The last two can be factorized into the product of half-indices. We show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/agh1q-xw932Trialities of minimally supersymmetric 2d gauge theories
https://resolver.caltech.edu/CaltechAUTHORS:20200413-094559729
Authors: {'items': [{'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Putrov-P', 'name': {'family': 'Putrov', 'given': 'Pavel'}}]}
Year: 2020
DOI: 10.1007/JHEP04(2020)079
We study dynamics of two-dimensional N = (0, 1) supersymmetric gauge theories. In particular, we propose that there is an infrared triality between certain triples of theories with orthogonal and symplectic gauge groups. The proposal is supported by matching of anomalies and elliptic genera. This triality can be viewed as a (0, 1) counterpart of the (0, 2) triality proposed earlier by two of the authors and A. Gadde. We also describe the relation between global anomalies in gauge theoretic and sigma-model descriptions, filling in a gap in the present literature.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2kwzk-b1v643d TQFTs from Argyres–Douglas theories
https://resolver.caltech.edu/CaltechAUTHORS:20180915-165620259
Authors: {'items': [{'id': 'Dedushenko-M', 'name': {'family': 'Dedushenko', 'given': 'Mykola'}, 'orcid': '0000-0002-9273-7602'}, {'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Nakajima-Hiraku', 'name': {'family': 'Nakajima', 'given': 'Hiraku'}}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Ye-Ke', 'name': {'family': 'Ye', 'given': 'Ke'}, 'orcid': '0000-0002-2978-2013'}]}
Year: 2020
DOI: 10.1088/1751-8121/abb481
We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres–Douglas theories on S¹ × M₃ with a non-trivial holonomy of a discrete global symmetry along the S¹. For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern–Simons and Rozansky–Witten types respectively. Changing the holonomy performs a Galois transformation on the TQFT, which can sometimes give rise to more familiar unitary theories such as the (G₂)₁ and (F₄)₁ Chern–Simons theories. Our construction is based on an intriguing relation between topologically twisted partition functions, wild Hitchin characters, and chiral algebras which, when combined together, relate Coulomb branch and Higgs branch data of the same 4d N = 2 theory. We test our proposal by applying localization techniques to the conjectural N = 1 UV Lagrangian descriptions of the (A₁, A₂), (A₁, A₃) and (A₁, D₃) theories.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bkvxa-xz107Generalized global symmetries of T[M] theories. Part I
https://resolver.caltech.edu/CaltechAUTHORS:20201111-130432310
Authors: {'items': [{'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Hsin-Po-Shen', 'name': {'family': 'Hsin', 'given': 'Po-Shen'}, 'orcid': '0000-0002-4764-1476'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}]}
Year: 2021
DOI: 10.1007/JHEP04(2021)232
We study reductions of 6d theories on a d-dimensional manifold M_d, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 − d)-dimensional theory T[M_d]. We refine and generalize the notion of "polarization" to polarization on M_d, which serves to fix the spectrum of local and extended operators in T[M_d]. Another important feature of theories T[M_d] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the 't Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/b9ndr-ppw424-manifolds and topological modular forms
https://resolver.caltech.edu/CaltechAUTHORS:20191014-080803922
Authors: {'items': [{'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Putrov-Pavel', 'name': {'family': 'Putrov', 'given': 'Pavel'}}, {'id': 'Vafa-Cumrun', 'name': {'family': 'Vafa', 'given': 'Cumrun'}}]}
Year: 2021
DOI: 10.1007/JHEP05(2021)084
We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on 't Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/tbg1f-ft873Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants
https://resolver.caltech.edu/CaltechAUTHORS:20210628-191053120
Authors: {'items': [{'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Hsin-Po-Shen', 'name': {'family': 'Hsin', 'given': 'Po-Shen'}, 'orcid': '0000-0002-4764-1476'}, {'id': 'Nakajima-Hiraku', 'name': {'family': 'Nakajima', 'given': 'Hiraku'}, 'orcid': '0000-0002-6060-758X'}, {'id': 'Park-Sunghyuk', 'name': {'family': 'Park', 'given': 'Sunghyuk'}, 'orcid': '0000-0002-6132-0871'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Sopenko-Nikita', 'name': {'family': 'Sopenko', 'given': 'Nikita'}, 'orcid': '0000-0002-8479-1924'}]}
Year: 2021
DOI: 10.1016/j.geomphys.2021.104311
By studying Rozansky-Witten theory with non-compact target spaces we find new connections with knot invariants whose physical interpretation was not known. This opens up several new avenues, which include a new formulation of q-series invariants of 3-manifolds in terms of affine Grassmannians and a generalization of Akutsu-Deguchi-Ohtsuki knot invariants.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bek1j-4v298Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups
https://resolver.caltech.edu/CaltechAUTHORS:20211206-191012374
Authors: {'items': [{'id': 'Gukov-S', 'name': {'family': 'Gukov', 'given': 'Sergei'}, 'orcid': '0000-0002-9486-1762'}, {'id': 'Pei-Du', 'name': {'family': 'Pei', 'given': 'Du'}, 'orcid': '0000-0001-5587-6905'}, {'id': 'Reid-Charles', 'name': {'family': 'Reid', 'given': 'Charles'}, 'orcid': '0000-0003-4598-5635'}, {'id': 'Shehper-Ali', 'name': {'family': 'Shehper', 'given': 'Ali'}, 'orcid': '0000-0002-3440-1721'}]}
Year: 2021
We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are 2d TQFTs whose fusion rules can be diagonalized. We show that, in this special basis, the 0-form symmetries always act as permutations while 1-form symmetries act by phases. This leads to an explicit description of the gauging of these symmetries. One application of our results is a generalization of the equivariant Verlinde formula to the case of general Lie groups. The generalized formula leads to many predictions for the geometry of Hitchin moduli spaces, which we explicitly check in several cases with low genus and SO(3) gauge group.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/ygk81-2jx08