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

Autor:	Gavrylenko, P., Lisovyy, O.
Rok vydání:	2017
Předmět:	Mathematical Physics High Energy Physics - Theory
Druh dokumentu:	Working Paper
Popis:	We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ 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 Painlev\'e 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. Comment: 20 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1705.01869 Zobrazit plný text záznamu View this record from Arxiv