Heterotic string solutions and coset conformal field theories

TL;DR

This paper explores heterotic string solutions related to coset conformal field theories, presenting exact backgrounds, analyzing their properties, and discussing dualities, with some solutions matching known models and others highlighting inconsistencies.

Contribution

It introduces new heterotic string backgrounds based on coset CFTs, examines their anomaly structure, and investigates duality properties, extending previous superstring solutions.

Findings

Exact left-right symmetric solutions with torsion gauge fields.

Identification of an anomaly in the (1,0) supersymmetric gauged WZNW theory.

A perturbative heterotic solution matching known models at leading order.

Abstract

We discuss solutions of the heterotic string theory which are analogous to bosonic and superstring backgrounds related to coset conformal field theories. A class of exact `left-right symmetric' solutions is obtained by supplementing the metric, antisymmetric tensor and dilaton of the superstring solutions by the gauge field background equal to the generalised Lorentz connection with torsion. As in the superstring case, these backgrounds are $\a'$-independent, i.e. have a `semiclassical' form. The corresponding heterotic string sigma model is obtained from the combination of the (1,0) supersymmetric gauged WZNW action with the action of internal fermions coupled to the target space gauge field. The pure (1,0) supersymmetric gauged WZNW theory is anomalous and does not describe a consistent heterotic string solution. We also find (to the order $\alpha'^3$) a two-dimensional perturbative heterotic string solution with the trivial gauge field background. To the leading order in $\alpha'$ it coincides with the known $SL(2,R)/U(1)$ bosonic or superstring solutions. This solution does not correspond to a `heterotic' combination of the left superstring and right bosonic $L_0$-operators at the conformal field theory level. Some duality properties of the heterotic string solutions are studied.