Linear Models for Flux Vacua

TL;DR

The paper develops torsion linear sigma models (TLSMs) to realize heterotic flux vacua with nonzero $H$-flux as IR limits of $2d$ gauge theories, using a 2d Green–Schwarz mechanism to cancel gauge anomalies. This framework yields compact Fu–Yau-type geometries as the IR target spaces, linking worldsheet dynamics to non-Kähler manifolds and Bianchi identities via anomaly cancellation. The authors analyze both non-compact and compact constructions, derive Bianchi-consistency conditions, discuss global and spacetime anomaly constraints, and argue for IR conformal fixed points, providing a microscopic CFT description of Fu–Yau and related KST-type vacua. They also identify limitations (e.g., base choices like $S=T^4$) and outline future work on instanton stability, moduli, and dualities, with potential extensions to higher-dimensional bases and non-CY geometries.

Abstract

We construct worldsheet descriptions of heterotic flux vacua as the IR limits of N=2 gauge theories. Spacetime torsion is incorporated via a 2d Green-Schwarz mechanism in which a doublet of axions cancels a one-loop gauge anomaly. Manifest (0,2) supersymmetry and the compactness of the gauge theory instanton moduli space suggest that these models, which include Fu-Yau models, are stable against worldsheet instanton effects, implying that they, like Calabi-Yaus, may be smoothly extended to solutions of the exact beta functions. Since Fu-Yau compactifications are dual to KST-type flux compactifications, this provides a microscopic description of these IIB RR-flux vacua.