Linear Sigma Models with Torsion

TL;DR

This paper develops a linear construction of torsional heterotic compactifications using gauged linear sigma models with (0,2) supersymmetry, enabling new models with fluxes and branes, including non-Kähler spaces.

Contribution

It introduces a novel linear framework for torsional heterotic compactifications, extending symplectic reduction to non-Kähler spaces with fluxes and branes.

Findings

Constructed a family of metrics deforming the heterotic conifold with H-flux.

Developed gauge-invariant compact models at the quantum level.

Presented a generalization of symplectic reduction for non-Kähler spaces.

Abstract

Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of couplings than models with (2,2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models with branes. As a non-compact example, we describe a family of metrics which correspond to deformations of the heterotic conifold by turning on H-flux. We then describe compact models which are gauge-invariant only at the quantum level. Our construction gives a generalization of symplectic reduction. The resulting spaces are non-Kahler analogues of familiar toric spaces like complex projective space. Perturbatively conformal models can be constructed by considering intersections.