Heterotic sigma models on T⁸ and the Borcherds automorphic form Φ₁₂

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.