3d Expansions of 5d Instanton Partition Functions

TL;DR

This paper introduces new ways to expand 5d instanton partition functions into 3d gauge theory components, linking them to BPS/CFT correspondence and generalizing previous results.

Contribution

It presents novel expansions of Nekrasov's instanton partition functions for 5d theories into 3d subspace partition functions, connecting to $W_{q,t}$ correlators and extending prior work.

Findings

New expansions of 5d instanton partition functions into 3d gauge theories.

Matching of these expansions with $W_{q,t}$ correlators involving screening charges.

Generalization and interpolation of existing results in the literature.

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 $\mathbb{C}^2_{q,t^{-1}} \times \mathbb{S}^1$, 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.