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.File in questo prodotto:
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