Green-Schwarz mechanism in heterotic (2,0) gauged linear sigma models: torsion and NS5 branes

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 nongauge 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.

The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications

“…Compactification of the E 8 × E 8 heterotic string [1,2,3] and heterotic M-theory [4]- [9] on Calabi-Yau threefolds has provided a rich arena for string phenomenology [10]- [30]. However, moduli stabilization in such theories has remained a crucial and long-standing problem.…”

On marginal deformations of (0,2) non-linear sigma models

“…The latter would be especially interesting for the linear sigma models appropriate for flux backgrounds [27][28][29].…”

Heterotic mini-landscape in blow-up

“…This is based on the fact that the Bianchi Identities (BI) giving a consistent gauge flux, possess strong similarities with the mass equations of the orbifold states. In the gauged linear sigma model description [40] the mass equation appears as the anomaly cancellation condition [41,42]. Those results, opened a way to study the transition in a more precise manner.…”

“…This set of equations allows us to explore if a given orbifold model has candidates for blow-up modes fulfilling the Bianchi Identities, which are conjectured to be linked to the orbifold mass equations [39,41,42]. This exploration can be performed in a reasonable computing time.…”