Chiral gauged WZNW models and heterotic string backgrounds

TL;DR

This paper constructs new heterotic string backgrounds using chiral gauged WZNW models, revealing their conformal invariance, supersymmetric extensions, and exact couplings, including a heterotic analogue of the black string solution.

Contribution

It introduces and analyzes chiral gauged WZNW models for heterotic strings, showing their conformal invariance, supersymmetric extension, and exact coupling forms, differing from standard models.

Findings

Chiral gauged WZNW models are conformally invariant despite lacking the usual gauge invariance.

The (1,0) supersymmetric extension of these models is consistent at the quantum level.

Explicit heterotic string background solutions, including a heterotic black string, are derived.

Abstract

We construct new heterotic string backgrounds which are analogous to superstring solutions corresponding to coset models but are not simply the `embeddings'of the latter. They are described by the (1,0) supersymmetric extension of the $G/H$ chiral gauged WZNW models. The `chiral gauged' WZNW action differs from the standard gauged WZNW action by the absence of the $A\bar A$-term (and thus is not gauge invariant in the usual sense) but can still be expressed as a combination of WZNW actions and is conformal invariant. We explain a close relation between gauged and chiral gauged WZNW models and prove that in the case of the abelian $H$ the $G/H$ chiral gauged theory is equivalent to a particular $(G\times H)/H$ gauged WZNW theory. In contrast to the gauged WZNW model, the chiral gauged one admits a (1,0) supersymmetric extension which is consistent at the quantum level. Integrating out the $2d$ gauge field we determine the exact (in $\alpha'$) form of the couplings of the corresponding heterotic sigma model. While in the bosonic (superstring) cases all the fields depend (do not depend) non-trivially on $\alpha'$ here the metric receives only one $O(\alpha')$ correction while the antisymmetric tensor and the dilaton remain semiclassical. As a simplest example, we discuss the basic $D=3$ solution which is the heterotic string counterpart of the `black string' $SL(2,R) \times R/ R $ background.