Circular quiver gauge theories, isomonodromic deformations and WN fermions on the torus

Giulio Bonelli, Fabrizio Del Monte, Pavlo Gavrylenko, Alessandro Tanzini

Research output: Contribution to journalArticlepeer-review

Abstract

We study the relation between class S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two-dimensional torus with punctures. Turning on the self-dual Ω -background corresponds to a deautonomization of the Seiberg–Witten integrable system which implies a specific time dependence in its Hamiltonians. We show that the corresponding τ-function is proportional to the dual gauge theory partition function, the proportionality factor being a nontrivial function of the solution of the deautonomized Seiberg–Witten integrable system. This is obtained by mapping the isomonodromic deformation problem to WN free fermion correlators on the torus.

Original languageEnglish
Article number83
JournalLetters in Mathematical Physics
Volume111
Issue number3
DOIs
Publication statusPublished - Jun 2021

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