Surface defects and elliptic quantum groups

Yagi, Junya

doi:10.1007/jhep06(2017)013

Cited by 37 publications

(62 citation statements)

References 77 publications

(160 reference statements)

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“…For example, we can dimensionally reduce the theory along some directions of the compactification manifold, or we can integrate out some matters by giving mass. As long as these operations preserve the duality 28 , one should land 28 Since the Yang-Baxter duality is an IR duality, it is a non-trivial question whether flowing to the IR and dimensional reduction commute. See [72] for a related discussion.…”

Section: General Lessonsmentioning

confidence: 99%

“…The actual integrable model has been discussed in many papers in the literature. While it is difficult to precisely summarize the rich literature, it might be useful for readers to loosely classify the literature into: 4d N = 1 on S 1 × S 3 [14,15,16,11,12,17,24,23,28], on S 1 × S 3 Z r [13,25,21,22,29], 3d N = 2 on S 1 × S 2 [18,20,27,31], on S 3 [76,11,12] and S 3 Z r [22], 2d N = (2, 2) on S 2 [26], on T 2 [18,19,30], and 1d N = 4 on S 1 [26].…”

Section: New Integrable Modelsmentioning

confidence: 99%

“…Another peculiar feature of the model is that it does not have the rapidity difference property 37 Note that the integrable models discussed in the work of Nekrasov and Shatashvili [99] and also of Costello [4] is the six-vertex model (Heisenberg XXZ spin chain) and its generalizations, which are themselves of different class from the chiral Potts models and their generalizations discussed in this lecture. However, there is a known connection between chiral Potts model and the six-vertex model due to Bazhanov and Stroganov [100], and one expects that this will be the key for finding appropriate relations with the Gauge/YBE correspondence (see [28] for recent related discussion). (4).…”

Section: Root-of-unity Limitmentioning

confidence: 99%

“…There are by now substantial literature on this subject, see e.g [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]…”

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confidence: 99%

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Integrability as duality: The Gauge/YBE correspondence

Yamazaki

2020

Physics Reports

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The Gauge/YBE correspondence states a surprising connection between solutions to the Yang-Baxter equation with spectral parameters and partition functions of supersymmetric quiver gauge theories. This correspondence has lead to systematic discoveries of new integrable models based on quantum-field-theory methods. We provide pedagogical introduction to the subject and summarizes many recent developments. This is a write-up of the lecture at the String-Math 2018 conference.August 15, 2018

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Section: General Lessonsmentioning

confidence: 99%

Section: New Integrable Modelsmentioning

confidence: 99%

Section: Root-of-unity Limitmentioning

confidence: 99%

“…There are by now substantial literature on this subject, see e.g [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]…”

mentioning

confidence: 99%

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Integrability as duality: The Gauge/YBE correspondence

Yamazaki

2020

Physics Reports

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“…See also e.g[32,36,37,71,73,[97][98][99][100][101][102][103][104][105][106] for some generalizations and other examples of this construction for superconformal indices in the presence of vortex defects.…”

mentioning

confidence: 99%

An infrared bootstrap of the Schur index with surface defects

Fluder

Longhi

2019

J. High Energ. Phys.

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The infrared formula relates the Schur index of a 4d N = 2 theory to its wallcrossing invariant, a.k.a. BPS monodromy. A further extension of this formula, proposed by Córdova, Gaiotto and Shao, includes contributions by various types of line and surface defects. We study BPS monodromies in the presence of vortex surface defects of arbitrary vorticity for general class S theories of type A 1 engineered by UV curves with at least one regular puncture. The trace of these defect BPS monodromies is shown to coincide with the action of certain q-difference operators acting on the trace of the (pure) 4d BPS monodromy. We use these operators to develop a "bootstrap" (of traces) of BPS monodromies, relying only on their infrared properties, thereby reproducing the very general ultraviolet characterization of the Schur index.A relation between Schur indices and BPS monodromies was conjectured in [23], following 6 See also [45], for some results of an IR formula for the lens index. 9 The "no-exotics" property asserts that BPS states have R = 0 in 4d N = 2 gauge theories [33,54,55]. 10 In practice, BPS spectra at arbitrary moduli can be rather involved, and by moving onto a "simple" sector of the theory, in which one can explicitly compute the protected spin character, the wall-crossing formulae allow to extract the BPS degeneracies in other sectors. the latter reference are precisely the "vortex defects" considered in [31] via the Higgsing procedure (see also Appendix A.3), and in the present paper via the IR formalism.

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Defect multiplets of N = 1 $$ \mathcal{N}=1 $$ supersymmetry in 4d

Drukker

Shamir

Vergu

2018

J. High Energ. Phys.

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Any 4d theory possessing N = 1 supersymmetry admits a so called Smultiplet, containing the conserved energy-momentum tensor and supercurrent. When a defect is introduced into such a theory, the S-multiplet receives contributions localised on the defect, which indicate the breaking of some translation symmetry and consequently also some supersymmetries. We call this the defect multiplet. We classify such terms corresponding to half-BPS defects which can be either three-dimensional, preserving 3d N = 1, or two-dimensional, preserving N = (0, 2). The new terms localised on the defect furnish multiplets of the reduced symmetry and give rise to the displacement operator.

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Surface defects and elliptic quantum groups

Cited by 37 publications

References 77 publications

Integrability as duality: The Gauge/YBE correspondence

Integrability as duality: The Gauge/YBE correspondence

An infrared bootstrap of the Schur index with surface defects

Defect multiplets of N = 1 $$ \mathcal{N}=1 $$ supersymmetry in 4d

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