Green-Schwarz Mechanism in Heterotic (2,0) Gauged Linear Sigma Models: Torsion and NS5 Branes

TL;DR

This paper explores how field-dependent FI-terms in heterotic (2,0) GLSMs induce a Green-Schwarz mechanism on the worldsheet, leading to torsional geometries and NS5 brane configurations, constrained by anomaly and quantization conditions.

Contribution

It demonstrates the role of non-gauge invariant FI-terms in canceling anomalies and describes their connection to torsion and NS5 branes in heterotic string compactifications.

Findings

Field-dependent FI-terms can cancel worldsheet anomalies via a Green-Schwarz mechanism.

Logarithmic FI-terms correspond to NS5 branes in the target space.

Constraints from quantization restrict the allowed FI-term configurations.

Abstract

Heterotic string compactifications can be conveniently described in the language of (2,0) gauged linear sigma models (GLSMs). Such models allow for Fayet-Iliopoulos (FI)-terms, which can be interpreted as Kahler parameters and axions on the target space geometry. We show that field dependent non-gauge invariant FI-terms lead to a Green-Schwarz-like mechanism on the worldsheet which can be used to cancel worldsheet anomalies. However, given that these FI-terms are constrained by quantization conditions due to worldsheet gauge instantons, the anomaly conditions turn out to be still rather constraining. Field dependent non-gauge invariant FI-terms result in non-Kahler, i.e. torsional, target spaces in general. When FI-terms involve logarithmic terms, the GLSM seems to describe the heterotic string in the presence of Neveu-Schwarz (NS)5 branes. In particular, when the gauge bundle overcloses the Bianchi identities, the GLSM describes a decompactified target space geometry due to anti-NS5 branes.