Duality invariant class of exact string backgrounds

TL;DR

This paper identifies a class of exact string backgrounds invariant under $O(D,D)$ duality, connecting curved and flat solutions with non-trivial antisymmetric tensors and dilaton fields, and provides explicit examples including a 4D case related to a WZW model.

Contribution

It introduces a class of $2+D$-dimensional backgrounds with covariantly constant null Killing vectors that are invariant under $O(D,D)$ duality, with exact solutions unaffected by $ '$-corrections.

Findings

$O(D,D)$ duality connects curved backgrounds with flat metric solutions.

Exact solutions are unaffected by $ '$-corrections.

Explicit examples include a 4D background related to a WZW model.

Abstract

We consider a class of $2+D$ - dimensional string backgrounds with a target space metric having a covariantly constant null Killing vector and flat `transverse' part. The corresponding sigma models are invariant under $D$ abelian isometries and are transformed by $O(D,D)$ duality into models belonging to the same class. The leading-order solutions of the conformal invariance equations (metric, antisymmetric tensor and dilaton), as well as the action of $O(D,D)$ duality transformations on them, are exact, i.e. are not modified by $\a'$-corrections. This makes a discussion of different space-time representations of the same string solution (related by $O(D,D|Z)$ duality subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved $2+D$-dimensional backgrounds with solutions having flat metric but, in general, non-trivial antisymmetric tensor and dilaton. We discuss several particular examples including the $2+D=4$ - dimensional background that was recently interpreted in terms of a WZW model.