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 ${\mathbb{C}}_{q,t^{-1}}^2\times {\mathbb{S}}^1$, we show that the instanton partition function admits expansions in terms of partition functions of unitary gauge theories living on the 3d subspaces ${\mathbb{C}}_q\times {\mathbb{S}}^1$, ${\mathbb{C}}_{t^{-1}}\times {\mathbb{S}}^1$ and their intersection along ${\mathbb{S}}^1$. 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.

v1: 30 pages. v2: references added. v3:JHEP version with added references and clarifications

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