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

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

doi:10.1007/s11005-020-01343-4

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

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 W_N free fermion correlators on the torus.

Original language	English
Article number	83
Number of pages	38
Journal	Letters in Mathematical Physics
Volume	111
Issue number	3
DOIs	https://doi.org/10.1007/s11005-020-01343-4
Publication status	Published - 23 Jun 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-020-01343-4Licence: Creative Commons: Attribution (CC BY)

Cite this

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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.",

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AU - Gavrylenko, Pavlo

AU - Tanzini, Alessandro

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