Pure π‘†π‘ˆ(2) gauge theory partition function and generalized Bessel kernel

@article{Gavrylenko2017PureG,
  title={Pure π‘†π‘ˆ(2) gauge theory partition function
 and generalized Bessel kernel},
  author={Pavlo Gavrylenko and O Lisovyy},
  journal={Proceedings of Symposia in Pure
                        Mathematics},
  year={2017}
}
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.Β 
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