## 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 SL_{2} 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.

Original language | English |
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Pages (from-to) | 1381-1419 |

Number of pages | 39 |

Journal | Communications in Mathematical Physics |

Volume | 377 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jul 2020 |

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