Mock modular index of M2-M5 brane systems

Abstract

We present Bogomolny-Prasad-Sommerfield (BPS) indices of the supergroup Wess-Zumino-Witten (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 multivariable Appell-Lerch sum. It indicates that wall crossing occurs in the BPS state counting due to the C field on the M5-branes.