3d Expansions of 5d Instanton Partition Functions

Authors: Fabrizio Nieri, Yiwen Pan, Maxim Zabzine. Preprint Number: UUITP-43/17 We propose a set of novel expansions of Nekrasov’s instanton partition functions. Focusing on 5d N = 1 U(N) pure Yang-Mills theory on C(2)xS(1), we show that the instanton partition functions admit expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces (C(1)xS(1))\cup(C(1)xS(1)) and their intersection along S(1). These new expansions are natural from the BPS/CFT viewpoint, as they can be matched with W(q,t) correlators involving an arbitrary number of screening charges of two kinds. Our constructions generalize and interpolate existing results in the literature.