A Worldsheet Approach to $\mathbf{\mathcal{N}=1}$ Heterotic Flux Backgrounds

TL;DR

This paper develops a worldsheet description of heterotic flux backgrounds with minimal supersymmetry using gauged linear sigma-models, enabling analysis of singularity resolutions and symmetry constraints in these complex geometries.

Contribution

It introduces a GLSM framework for heterotic flux backgrounds with torsion, providing explicit constructions and symmetry analyses for orbifold geometries over K3 surfaces.

Findings

GLSM formulation for heterotic flux backgrounds

Explicit automorphism constructions of order two and three

Insights into singularity resolution in orbifold geometries

Abstract

Heterotic backgrounds with torsion preserving minimal supersymmetry in four dimensions can be obtained as orbifolds of principal $T^{2}$ bundles over $K3$. We consider a worldsheet description of these backgrounds as gauged linear sigma-models (GLSMs) with $(0,2)$ supersymmetry. Such a formulation provides a useful framework in order to address the resolution of singularities of the orbifold geometries. We investigate the constraints imposed by discrete symmetries on the corresponding torsional GLSMs. In particular, the principal $T^{2}$ connection over $K3$ is inherited from $(0,2)$ vector multiplets. As these vectors gauge global scaling symmetries of products of projective spaces, the corresponding $K3$ geometry is naturally realized as an algebraic hypersurface in such a product (or as a branched cover of it). We outline the general construction for describing such orbifolds. We give explicit constructions for automorphisms of order two and three.