The ALE Partition Functions of M-Strings

TL;DR

This paper calculates the equivariant partition function of six-dimensional M-string SCFTs on a background combining a torus and an ALE singularity, revealing new features of BPS string worldsheet theories influenced by discrete data.

Contribution

It introduces a novel computation of 6d M-string partition functions on ALE backgrounds, uncovering the role of relative field theories and discrete data in BPS string worldsheets.

Findings

Partition functions computed for M-string SCFTs on ALE backgrounds.

BPS string worldsheet theories are relative and sensitive to discrete data.

Results agree with a 6d Nekrasov master formula and known 4d ALE partition functions.

Abstract

We compute the equivariant partition function of the six-dimensional M-string SCFTs on a background with the topology of a product of a two-dimensional torus and an ALE singularity. We determine the result by exploiting BPS strings probing the singularity, whose worldvolume theories we determine via a chain of string dualities. A distinguished feature we observe is that for this class of background the BPS strings' worldsheet theories become relative field theories that are sensitive to finer discrete data generalizing to 6d the familiar choices of flat connections at infinity for instantons on ALE spaces. We test our proposal against a conjectural 6d N = (1,0) generalization of the Nekrasov master formula, as well as against known results on ALE partition functions in four dimensions.