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

@article{Gavrylenko2017PureG,
title={Pure 𝑆𝑈(2) gauge theory partition function
and generalized Bessel kernel},
author={Pavlo Gavrylenko and O Lisovyy},
journal={Proceedings of Symposia in Pure
Mathematics},
year={2017}
}
• Published 4 May 2017
• Mathematics
• Proceedings of Symposia in Pure Mathematics
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 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.
19 Citations

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