In this paper we study the extension of Painlevé/gauge theory correspondence to circular quivers by focusing on the special case of SU(2) N= 2 ∗ theory. We show that the Nekrasov–Okounkov partition function of this gauge theory provides an explicit combinatorial expression and a Fredholm determinant formula for the tau-function describing isomonodromic deformations of SL2 flat connections on the one-punctured torus. This is achieved by reformulating the Riemann–Hilbert problem associated to the latter in terms of chiral conformal blocks of a free-fermionic algebra. This viewpoint provides the exact solution of the renormalization group flow of the SU(2) N= 2 ∗ theory on self-dual Ω -background and, in the Seiberg–Witten limit, an elegant relation between the IR and UV gauge couplings. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

N=2*Gauge Theory, Free Fermions on the Torus and Painleve VI / Bonelli, Giulio; Del Monte, Fabrizio; Gavrylenko, Pavlo; Tanzini, Alessandro. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 377:2(2020), pp. 1381-1419. [10.1007/s00220-020-03743-y]

N=2*Gauge Theory, Free Fermions on the Torus and Painleve VI

Bonelli, Giulio;Del Monte, Fabrizio
;
Tanzini, Alessandro
2020

Abstract

In this paper we study the extension of Painlevé/gauge theory correspondence to circular quivers by focusing on the special case of SU(2) N= 2 ∗ theory. We show that the Nekrasov–Okounkov partition function of this gauge theory provides an explicit combinatorial expression and a Fredholm determinant formula for the tau-function describing isomonodromic deformations of SL2 flat connections on the one-punctured torus. This is achieved by reformulating the Riemann–Hilbert problem associated to the latter in terms of chiral conformal blocks of a free-fermionic algebra. This viewpoint provides the exact solution of the renormalization group flow of the SU(2) N= 2 ∗ theory on self-dual Ω -background and, in the Seiberg–Witten limit, an elegant relation between the IR and UV gauge couplings. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
377
2
1381
1419
https://link.springer.com/article/10.1007/s00220-020-03743-y
Bonelli, Giulio; Del Monte, Fabrizio; Gavrylenko, Pavlo; Tanzini, Alessandro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/116169
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