AdS vacua of non-supersymmetric strings

TL;DR

Raucci and Tomasiello study AdS vacua in three tachyon-free non-supersymmetric string theories by reducing the ten-dimensional equations to algebraic conditions through a constant dilaton and a universal three-form flux. They first construct new AdS backgrounds sourced by three-form flux in heterotic and orientifold setups, including AdS$_7$, AdS$_4$, and AdS$_5$ geometries with multiple internal factors, and they derive explicit flux-quantized radii relations. They then develop a Kaluza–Klein–inspired reduction on homogeneous coset spaces to incorporate large gauge fields, obtaining AdS$_4$ vacua on six-dimensional cosets (flag, CP$^3$, and S$^6$) with automatically satisfied Bianchi identities and nearly-Kähler internal geometry. Across these constructions, the resulting vacua are not scale-separated, and the framework highlights a generally applicable approach to engineering non-supersymmetric AdS backgrounds via KK reductions and fluxes in string theory.

Abstract

Few vacua are known for the three tachyon-free non-supersymmetric string theories. We find new classes of AdS backgrounds by focusing on spaces where the equations of motion reduce to purely algebraic conditions. Our first examples involve non-zero three-form fluxes supported either on direct product internal spaces or on $T_{p,q}$ geometries. For the ${\mathrm{SO}}(16)\times{\mathrm{SO}}(16)$ heterotic string, we then develop a method to engineer vacua with the addition of gauge fields. A formal Kaluza--Klein reduction yields complete solutions on a broad class of coset spaces $G/H$, automatically satisfying the three-form Bianchi identities with $H$-valued gauge fields.