Higgs Bundles, Gauge Theories and Quantum Groups

200

Bethe/gauge correspondence identifies supersymmetric vacua of massive gauge theories invariant under the two dimensional N = 2 Poincare supersymmetry with the stationary states of some quantum integrable system. The supersymmetric theory can be twisted in a number of ways, producing a topological field theory. For these theories we compute the handle gluing operator H. We also discuss the Gaudin conjecture on the norm of Bethe states and its connection to H.

Section: Acknowledgmentsmentioning

confidence: 92%

Section: Jhep01(2015)100mentioning

confidence: 99%

Section: Superpotential Deformations and Twisted Massesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bethe/gauge correspondence on curved spaces

Nekrasov

Shatashvili

2015

200

“…[67,84,94]. The particular implementations of this correspondence are well-known under the names of the AGT conjecture [2,120], and the Bethe/gauge correspondence [89,96] (see [43,44,74] for the prior work). For details the interested reader may consult the references in, e.g.…”

Section: Jhep03(2016)181mentioning

confidence: 99%

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Nekrasov

2016

210

466

We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the qq-characters. In the context of the BPS/CFT correspondence, using these observables, we derive an infinite set of Dyson-Schwinger-type relations. These relations imply that the supersymmetric partition functions in the presence of Ω-deformation and defects obey the Ward identities of two dimensional conformal field theory and its q-deformations. The details will be discussed in the companion papers.

Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS

Giombi

Pestun

2013

126

We study correlation functions of Wilson loops and local operators in a subsector of N = 4 SYM which preserves two supercharges. Localization arguments allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills theory. In turn, this can be reduced to computing correlators in certain Gaussian multi-matrix models. We focus on the correlation function of a Wilson loop and two local operators, and solve the corresponding three-matrix model exactly in the planar limit. We compare the strong coupling behavior to string theory in AdS 5 × S 5 , finding precise agreement. We pay particular attention to the case in which the local operators have large R-charge J ∼ √ λ at strong coupling. * On leave of absence from ITEP, 117218, Moscow, Russia IntroductionExact results in non-abelian gauge theories are rare and clearly of great importance. In supersymmetric gauge theories, the powerful technique of localization allows sometimes for such exact results for certain observables preserving some fermionic symmetries of the theory. For example the exact expressions conjectured in [1, 2] for the circular 1/2-BPS Wilson loop in N = 4 SYM were proved using localization in [3], as well as extendend to a large class of N = 2 theories.In N = 4 SYM, a wide generalization of the 1/2-BPS circle to lower supersymmetric Wilson loops of arbitrary shapes was introduced in [4-6] and then classified in [7]. An interesting subfamily of that construction consists of operators supported on any loop on a two-sphere S 2 embedded into the R 4 spacetime. Generically, these Wilson loops are 1/8-BPS, and it was conjectured in [4][5][6] that their quantum correlators are exactly captured by a purely perturbative calculation in bosonic 2d Yang-Mills. The conjecture was later strongly supported by the localization calculation in [8], where it was shown that the path-integral with insertions of those loop operators localizes on a 2d gauge theory closely related to the Hitchin/Higgs-Yang Mills system [9][10][11], which can be seen to be perturbatively equivalent to ordinary bosonic 2d Yang-Mills. 2 The calculation in the 2d theory can be then mapped to certain Gaussian multi-matrix models, which allow for an exact evaluation of the correlators. Several checks of the relation to 2d YM have appeared [12][13][14][15][16][17]. 3 In particular, recently the localization result for the expectation value of a Wilson loop in this family was used in [18] (see also [19]) to derive an exact expression for the low-angle limit of the cusp anomalous dimension. This has been checked using integrability up to three loops in [20] (see also [21]) and analytically to all loops in [22], providing a first link between localization and integrability results.The calculation in [8] also suggested that localization applies in fact not only to the Wilson loops, but to a larger sector of operators that are annihilated by the same supercharge. This include certain chiral primary operators inserted on the S 2 [23] as well as 't Hooft loops linked with the S 2 [24]. T...