Mock Modularity Of Twisted Index In CHL Models

TL;DR

This paper investigates the twisted partition function of quarter BPS states in CHL models, revealing that microstate degeneracies relate to mock Jacobi forms, extending previous work on BPS dyons in string theory.

Contribution

It demonstrates that for many single-centered black holes in CHL models, microstate degeneracies are given by Fourier coefficients of mock Jacobi forms, and introduces multiplicative and additive lift constructions.

Findings

Microstate degeneracies linked to mock Jacobi forms.

Extension of DMZ and BSS frameworks to CHL models.

Construction methods for the partition function via lifts.

Abstract

We study the twisted partition function of quarter BPS states in CHL models and show that for a large class of single-centered black holes, the degeneracy of microstates is given by the Fourier coefficients of mock Jacobi forms. Our analysis is a continuation of the programme initiated by Dabholkar, Murthy and Zagier (DMZ) for $1/4$-BPS dyons in $\mathcal{N} = 4$ string theory and further extended by Bhand, Sen and Singh (BSS) to quarter BPS states in CHL models. We also present the multiplicative lift construction of the partition function and comment on the additive lift of the same.