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

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Abstract

We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ 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 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.
Original languageEnglish
Title of host publicationString-Math 2016
EditorsAmir-Kian Kashani-Poor, Ruben Minasian, Nikita Nekrasov, Boris Pioline
Place of PublicationProvidence, RI
PublisherAmerican Mathematical Society
Volume98
ISBN (Electronic)978-1-4704-4770-0
ISBN (Print)978-1-4704-3515-8
DOIs
Publication statusPublished - 4 May 2017

Publication series

NameProceedings of Symposia in Pure Mathematics
PublisherAmerican Mathematical Society
Volume98
ISSN (Print)0082-0717
ISSN (Electronic)2324-707X

Bibliographical note

20 pages, 6 figures

Keywords

  • math-ph
  • hep-th

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