On the Supersymmetric Index of the M-theory 5-brane and Little String Theory

TL;DR

This paper develops a six-dimensional framework to compute the supersymmetric index of M-theory 5-branes on complex geometries, incorporating self-dual tensors and little string states, matching known results and exploring moduli spaces.

Contribution

It introduces a novel six-dimensional approach to calculate the supersymmetric index of M5-branes, including contributions from self-dual tensors and little strings, extending to general geometries.

Findings

Reproduces known supersymmetric index results for specific geometries.

Provides a geometric interpretation of the moduli space of multi M5-branes.

Suggests a general structure for the index in broader settings.

Abstract

We propose a six-dimensional framework to calculate the supersymmetric index of M-theory 5-branes wrapped on a six-manifold with product topology $M_4\times T^2$, where $M_4$ is a holomorphic 4-cycle in a Calabi-Yau three-fold. This is obtained by zero-modes counting of the self-dual tensor contribution plus ``little'' string states and correctly reproduces the known results which can be obtained by shrinking or blowing the $T^2$ volume parameter. We also extract the geometric moduli space of the multi M5-brane system and infer the generic structure of the supersymmetric index for more general geometries.