We show that the dual partition function of the pure N = 2 SU (2) gauge theory in the self-dual Omega-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painleve III equation of type D-8 (radial sine-Gordon equation). In particular, the principal minor expansion of the Fredholm determinant yields Nekrasov combinatorial sums over pairs of Young diagrams.

Pure SU(2) gauge theory partition function and generalized Bessel kernel / Gavrylenko, P.; Lisovyy, O.. - 98:(2018), pp. 181-205. [10.1090/pspum/098/01727]

Pure SU(2) gauge theory partition function and generalized Bessel kernel

Gavrylenko, P.;
2018-01-01

Abstract

We show that the dual partition function of the pure N = 2 SU (2) gauge theory in the self-dual Omega-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painleve III equation of type D-8 (radial sine-Gordon equation). In particular, the principal minor expansion of the Fredholm determinant yields Nekrasov combinatorial sums over pairs of Young diagrams.
2018
String-Math 2016
98
181
205
9781470435158
9781470447700
dx.doi.org/10.1090/PSPUM/098/01727
AMER MATHEMATICAL SOC
Gavrylenko, P.; Lisovyy, O.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135650
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