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 Oleg Lisovyy},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
  • Pavlo Gavrylenko, Oleg Lisovyy
  • Published 2017
  • Mathematics, Physics
  • arXiv: Mathematical Physics
  • 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. 

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