3d expansions of 5d instanton partition functions

Abstract

We propose a set of novel expansions of Nekrasov’s instanton partition functions. Focusing on 5d supersymmetric pure Yang-Mills theory with unitary gauge group on ℂq,t−12×S1, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces ℂ q× S1, ℂt−1×S1 and their intersection along S1. These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with Wq,t correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.