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

TL;DR

This work develops a microscopic description of heterotic $(2,0)$ compactifications via gauged linear sigma models with field-dependent FI terms. By implementing a worldsheet Green–Schwarz mechanism, the authors show how gauge anomalies can be canceled under specific conditions, though instanton quantization tightly constrains the allowed couplings. The framework reveals that such FI terms generally induce non-Kähler (torsion) target spaces, with logarithmic terms signaling NS5-branes and, in some phases, anti-NS5 branes causing decompactification. They connect these worldsheet constructions to orbifold–CY transitions, providing concrete examples on the quintic and on $\mathbb{P}^7[2,2,2,2]$, thus linking NS5-brane physics, torsion, and heterotic flux vacua in a unified GLSM setting.

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.