A note on mock automorphic forms and the BPS index

TL;DR

This paper explores the representation-theoretic aspects of mock automorphic forms, their potential generalizations, and their connection to BPS black hole counts, highlighting new perspectives in automorphic form theory and physics.

Contribution

It introduces a cohomological perspective on mock automorphic forms and discusses their growth properties and physical relevance to BPS black hole counting.

Findings

Mock automorphic forms relate to nontrivial $(\mathfrak{g},K)$-cohomology.

Replacing holomorphicity with cohomological conditions allows for growing Fourier coefficients.

Connection established between mock automorphic forms and BPS black hole counts.

Abstract

We discuss mock automorphic forms from the point of view of representation theory, that is, obtained from weak harmonic Maass forms give rise to nontrivial $(\mathfrak{g},K)$-cohomology. We consider the possibility of replacing the `holomorphic' condition with `cohomological' when generalizing to general reductive groups. Such a candidate allows for growing Fourier coefficients, in contrast to automorphic forms under the Miatello-Wallach conjecture. In the second part, we provide an overview of the connection with BPS black hole counts as a physical motivation for studying mock automorphic forms.