@inproceedings{9aa6931fe2484de8a0f89bde308c4098,
title = "Pure \$SU(2)\$ gauge theory partition function and generalized Bessel kernel",
abstract = "We show that the dual partition function of the pure \$\textbackslash{}mathcal N=2\$ \$SU(2)\$ gauge theory in the self-dual \$Ω\$-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.",
keywords = "math-ph, hep-th",
author = "P. Gavrylenko and O. Lisovyy",
note = "20 pages, 6 figures",
year = "2017",
month = may,
day = "4",
doi = "10.1090/pspum/098/01727",
language = "English",
isbn = "978-1-4704-3515-8",
volume = "98",
series = "Proceedings of Symposia in Pure Mathematics",
publisher = "American Mathematical Society",
editor = "Amir-Kian Kashani-Poor and Ruben Minasian and Nikita Nekrasov and Boris Pioline",
booktitle = "String-Math 2016",
address = "United States",
}