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

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 equa...

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Hauptverfasser:	Gavrylenko, P, Lisovyy, O
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Schlagworte:	Mathematics - Mathematical Physics Physics - High Energy Physics - Theory Physics - Mathematical Physics
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creator	Gavrylenko, P Lisovyy, O
description	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.
doi_str_mv	10.48550/arxiv.1705.01869
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title	Pure $SU(2)$ gauge theory partition function and generalized Bessel kernel
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