Exact four-dimensional string solutions and Toda-like sigma models from ‘null-gauged’ WZNW theories

Abstract

We construct a new class of exact string solutions with a four-dimensional target space metric of signature (−, +, +, +) by gauging the independent left and right nilpotent subgroups with ‘null’ generators of WZNW models for rank-2 non-compact groups G. The ‘null’ property of the generators (Tr( N n N m ) = 0) implies the consistency of the gauging and the absence of α′-corrections to the semiclassical backgrounds obtained from the gauged WZNW models. In the case of the maximally non-compact groups ( G = SL(3), SO(2,2), SO(2, 3), G 2) the construction corresponds to gauging some of the subgroups generated by the nilpotent ‘step’ operators in the Gauss decomposition. The rank-2 case is a particular example of a general construction leading to conformal backgrounds with one time-like direction. The conformal theories obtained by integrating out the gauge field can be considered as sigma model analogs of Toda models (their classical equations of motion are equivalent to Toda model equations). The procedure of ‘null gauging’ applies also to other non-compact groups. As an example, we consider the gauging of SO(1, 3) where the resulting metric has the signature (−, −, +, +) but admits two analytic continuations with Minkowski signature. The backgrounds we find have ‘2 + 2’ structure with two null Killing vectors. Their dual counterparts have one covariantly constant null Killing vector, i.e. are of ‘plane-wave’ type (with metric and dilation depending only on transverse spatial coordinates) and also represent exact string solutions.