Classical scale-separated AdS$_3$ vacua in heterotic string theory

TL;DR

The paper delivers the first fully classical scale-separated $AdS_3$ vacua in heterotic string theory by compactifying on $G_2$ structure manifolds with $H$ flux and smeared gravitational instantons. A 3D $\\mathcal{N}=1$ effective theory is derived from the heterotic action, and a large quantized flux $h_7$ in combination with non-closed $H$ flux yields weak coupling and large volume, enabling scale separation where the internal KK scale decouples from the AdS radius. A concrete nilmanifold example on $T^7/\\mathbb{Z}_2^3$ demonstrates explicit moduli stabilization, negative vacuum energy, and an $L_{KK}/L_{AdS} \\sim 1/N$ separation in the large $N$ limit under $1\\ll N^5\\ll h_7$, with all fluxes quantized and a smeared tadpole cancellation condition satisfied. The work provides a promising heterotic path to scale-separated AdS vacua and motivates future work on localized sources and potential worldsheet descriptions.

Abstract

We provide the first scale-separated AdS solutions from compactifications of the heterotic string. Our solutions have parametrically weak coupling, large volume, and the internal KK scale is parametrically smaller than the AdS length. These AdS$_3$ vacua preserve $\mathcal{N}=1$ supersymmetry and arise from compactifications on $G_2$ structure manifolds with $H$ flux and (smeared) gravitational instantons. All geometric moduli are stabilized, fluxes quantized, and the solutions are parametrically controlled in an appropriate large-flux limit.