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Heterotic string compactifications can be conveniently described in thelanguage of (2,0) gauged linear sigma models (GLSMs). Such models allow forFayet-Iliopoulos (FI)-terms, which can be interpreted as Kahler parameters andaxions on the target space geometry. We show that field dependent non-gaugeinvariant FI-terms lead to a Green-Schwarz-like mechanism on the worldsheetwhich can be used to cancel worldsheet anomalies. However, given that theseFI-terms are constrained by quantization conditions due to worldsheet gaugeinstantons, 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 ofNeveu-Schwarz (NS)5 branes. In particular, when the gauge bundle overcloses theBianchi identities, the GLSM describes a decompactified target space geometrydue to anti-NS5 branes.

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