Pure $SU(2)$ gauge theory partition function and generalized Bessel kernel
Abstract
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 Painlevé 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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2017
- DOI:
- 10.48550/arXiv.1705.01869
- arXiv:
- arXiv:1705.01869
- Bibcode:
- 2017arXiv170501869G
- Keywords:
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- Mathematical Physics;
- High Energy Physics - Theory
- E-Print:
- 20 pages, 6 figures