Recursive method for the Nekrasov partition function for classical Lie groups

Abstract

The Nekrasov partition function for supersymmetric gauge theories with general Lie groups is, so far, not known in a closed form, while there is a definition in terms of the integral. In this paper, as an intermediate step to derive the closed form, we give a recursion formula among partition functions, which can be derived from the integral. We apply the method to a toy model that reflects the basic structure of partition functions for ${\textit {BCD}}$-type Lie groups and obtain a closed expression for the factor associated with the generalized Young diagram.