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 Kähler 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-Kähler, 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, the GLSM leads to a decompactified target space geometry when anti-NS5 branes are present.
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