Heterotic sigma models on $T^8$ and the Borcherds automorphic form $\Phi_{12}$

TL;DR

This paper explores the spectrum of BPS states in heterotic sigma models on T^8, revealing a deep connection to Borcherds' automorphic form Φ_{12} and discussing implications for moonshine and AdS_3 gravity.

Contribution

It establishes a link between BPS state counting in heterotic T^8 sigma models and Borcherds' automorphic form Φ_{12}, highlighting novel mathematical-physical connections.

Findings

Counting function related to Φ_{12} automorphic form

Connection to automorphy for O(2,26;Z)

Implications for Umbral moonshine and AdS_3 gravity theories

Abstract

We consider the spectrum of BPS states of the heterotic sigma model with $(0,8)$ supersymmetry and $T^8$ target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds' automorphic form $\Phi_{12}$, a modular form which exhibits automorphy for $O(2,26;{\mathbb Z})$. We comment on possible implications for Umbral moonshine and theories of AdS$_3$ gravity.