N = 2∗ Gauge Theory, Free Fermions on the Torus and Painlevé VI
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 S L2 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.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- March 2020
- DOI:
- 10.1007/s00220-020-03743-y
- arXiv:
- arXiv:1901.10497
- Bibcode:
- 2020CMaPh.377.1381B
- Keywords:
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- High Energy Physics - Theory;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 40 pages, 6 figures