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

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.

12 pages; v2 error (involving fermion zero modes) corrected

References in corpus (3)

• Notes on the K3 Surface and the Mathieu group M_24
• Elliptic Genera and 3d Gravity
• Protected couplings and BPS dyons in half-maximal supersymmetric string vacua

Cited by in corpus (5)

• Exploring the landscape of heterotic strings on T^d
• BPS Algebras in 2D String Theory
• A Borcherds-Kac-Moody superalgebra with Conway symmetry
• Fun with $F_{24}$
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model