Circular quiver gauge theories, isomonodromic deformations and W_N\n fermions on the torus

2019/01/01 by Giulio Bonelli, Fabrizio Del Monte, Bonelli, Giulio +5 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.1909.07990

openalex publication_date 2019/01/01 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We study the relation between class S theories on punctured tori and\nisomonodromic deformations of flat SL(N) connections on the two dimensional\ntorus with punctures. Turning on the self dual \Ω-background corresponds\nto a deautonomization of the Seiberg-Witten integrable system which implies a\nspecific time dependence in its Hamiltonians. We show that the corresponding\n\τ-function is proportional to the dual gauge theory partition function,\nthe proportionality factor being a non trivial function of the solution of the\ndeautonomized Seiberg-Witten integrable system. This is obtained by mapping the\nisomonodromic deformation problem to W_N free fermion correlators on the\ntorus.\n

Citations

• Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations
• The Dependence on the Monodromy Data of the Isomonodromic Tau Function
• Classical and quantum conformal field theory

Cited by

• Modular transformations of tau functions and conformal blocks on the torus
• On a 5D UV completion of Argyres-Douglas theories

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