Pure $SU(2)$ gauge theory partition function and generalized Bessel kernel - Archive ouverte HAL Access content directly
Conference Papers Year : 2018

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

P. Gavrylenko
  • Function : Author

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 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.

Dates and versions

hal-01823332 , version 1 (26-06-2018)

Identifiers

Cite

P. Gavrylenko, O. Lisovyy. Pure $SU(2)$ gauge theory partition function and generalized Bessel kernel. String Math 2016, Jun 2016, Paris, France. pp.181-208. ⟨hal-01823332⟩
67 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More