Mock Modular Index of M2-M5 Brane System

TL;DR

This paper introduces BPS indices for supergroup WZW models on intersecting M2-M5 branes, revealing their expression via mock theta functions and indicating wall-crossing phenomena in BPS state counting.

Contribution

It provides explicit formulas for BPS indices in specific supergroup WZW models, connecting them to mock theta functions and demonstrating wall-crossing effects.

Findings

BPS indices expressed through mock theta functions.

Explicit formula for $PSL(2|2)_{k=1}$ WZW model.

Wall-crossing in BPS state counting due to $C$-field.

Abstract

We present BPS indices of the supergroup WZW models that live on intersecting M2-M5 brane systems. They can encode data of the stretched M2-branes between M5-branes and count the BPS states. They are generally expressed in terms of mock theta functions via the Kac-Wakimoto character formula of the affine Lie superalgebra. We give an explicit expression of the index for the $PSL(2|2)_{k=1}$ WZW model in terms of the second order multi-variable Appell-Lerch sum. It indicates that wall-crossing occurs in the BPS state counting due to the $C$-field on the M5-branes.