The Enhancement of Supersymmetry in M-strings

TL;DR

This paper investigates M-strings arising from M5-branes on an ALE space, demonstrating supersymmetry enhancement from (0) to (4) through parameter tuning, and explores alternative enhancement scenarios.

Contribution

It introduces a brane configuration on an ALE space, computes the M-string partition function using refined topological vertex, and reveals supersymmetry enhancement mechanisms.

Findings

Supersymmetry of M-strings enhances from (0) to (4) with parameter tuning.

Partition function computed via refined topological vertex formalism.

Discussion of alternative supersymmetry enhancement scenarios.

Abstract

We study two M5-branes on $A_{1}$ ALE space. We introduce some M2-branes suspended between the M5-branes. Then, the boundaries of M2-branes look like strings. We call them "M-strings". The M-strings have $\mathcal{N}=(4,0)$ supersymmetry by considering the brane configuration on $A_{1}$ ALE space. We calculate the partition function of M-strings by using the refined topological vertex formalism. We find that the supersymmetry of M-strings gets enhanced to $\mathcal{N}=(4,4)$ by tuning some K\"ahler parameters. Furthermore, we discuss another possibility of the enhancement of supersymmetry which is different from the above one.