Wilson-’t Hooft lines as transfer matrices

A bstract We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional N = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expe...

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Bibliographic Details
Published in:The journal of high energy physics 2021-01, Vol.2021 (1), p.1-31, Article 72
Main Authors: Maruyoshi, Kazunobu, Ota, Toshihiro, Yagi, Junya
Format: Article
Language:English
Subjects:
Brane Dynamics in Gauge Theories
Classical and Quantum Gravitation
Elementary Particles
Field theory
Field theory (physics)
Gauge theory
High energy physics
Lattice Integrable Models
Localization
Operators
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Supersymmetric Gauge Theory
Supersymmetry
Transfer matrices
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Summary:A bstract We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional N = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product space S 1 × ϵ ℝ 2 × ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP01(2021)072