The fate of discrete torsion on resolved heterotic Z2xZ2 orbifolds using (0,2) GLSMs

TL;DR

This paper investigates how discrete torsion behaves when heterotic orbifolds are smoothed into geometries using (0,2) GLSMs, revealing anomalies and flux implications in the process.

Contribution

It introduces novel resolution GLSMs for T6/Z2xZ2 and analyzes the effects of discrete torsion and H-flux in heterotic orbifold resolutions.

Findings

Non-compact orbifold GLSMs with/without torsion are largely equivalent.

Field redefinition anomalies reproduce discrete torsion phases.

Torsional compact orbifold GLSM exhibits mixed gauge anomalies.

Abstract

This paper aims to shed light on what becomes of discrete torsion within heterotic orbifolds when they are resolved to smooth geometries. Gauged Linear Sigma Models (GLSMs) possessing (0,2) worldsheet supersymmetry are employed as interpolations between them. This question is addressed for resolutions of the non-compact C3/Z2xZ2 and the compact T6/Z2xZ2 orbifolds to keep track of local and global aspects. The GLSMs associated with the non-compact orbifold with or without torsion are to a large extent equivalent: only when expressed in the same superfield basis, a field redefinition anomaly arises among them, which in the orbifold limit reproduces the discrete torsion phases. Previously unknown, novel resolution GLSMs for T6/Z2xZ2 are constructed. The GLSM associated with the torsional compact orbifold suffers from mixed gauge anomalies, which need to be cancelled by appropriate logarithmic superfield dependent FI-terms on the worldsheet, signalling H-flux due to NS5-branes supported at the exceptional cycles.