Four Dimensional Plane Wave String Solutions with Coset CFT Description

TL;DR

This paper constructs and analyzes four-dimensional string solutions with covariantly constant null Killing vectors, using coset conformal field theories and duality transformations, revealing new exact plane wave solutions with supersymmetry.

Contribution

It introduces a class of exact D=4 string solutions with null Killing vectors derived from coset models and dualities, expanding the landscape of known string backgrounds.

Findings

Constructed new exact plane wave solutions including Nappi-Witten model

Applied non-abelian duality to generate solutions with null Killing vectors

Found supersymmetric heterotic string plane wave solutions

Abstract

We present a number of D=4 bosonic and heterotic string solutions with a covariantly constant null Killing vector which, like the solution of Nappi and Witten (NW), correspond to (gauged) WZW models and thus have a direct conformal field theory interpretation. A class of exact plane wave solutions (which includes the NW solution) is constructed by `boosting' the twisted products of two D=2 `cosmological' or `black-hole' cosets of SL(2,R) and SU(2). We describe a general limiting procedure by which one can construct new solutions with a covariantly constant null Killing vector starting with known string backgrounds. By applying a non-abelian duality transformation to the NW model we find a D=4 solution which has a covariantly constant null Killing vector but is not a plane wave. Higher dimensional bosonic backgrounds with isometries can be interpreted as lower dimensional backgrounds with extra gauge fields. Some of them are at the same time solutions of the heterotic string theory. In particular, the NW model represents also a D=3 `gravi-electromagnetic' heterotic string plane wave. In addition to the (1,1) supersymmetric embeddings of bosonic solutions we construct a number of non-trivial (1,0) supersymmetric exact D=4 heterotic string plane wave solutions some of which are related (by a boost and analytic continuation) to limiting cases of D=4 heterotic black hole solutions.