A Closed Bianchi I Universe in String Theory

A special Bianchi I universe is constructed in 4D string theory. Geometrically it represents a 3D anti-de-Sitter space crossed with a flat direction whereas in terms of an associated conformal field theory it is an extremal case of a gauged WZWN theory with target the coset SU(1, 1)×R2/R . Some of its properties are discussed. ∗ email: [email protected] † Address after Sep. 1, 1992: Dept. of Physics, Univ. of Alberta, Edmonton, Alta T6G 2J1, Canada Recently investigations of string theory have converged on the study of nontrivial backgrounds, in hope that new information on the structure of quantum gravity may be obtained. A method which has proven particularly helpful in discovering novel solutions is the construction of exact conformal field theories on the world-sheet via gauging the Wess-Zumino-Witten-Novikov (WZWN) sigma model defined on a group of appropriate topology. Since Witten’s demonstration that such approach, in case of the SL(2, R) group on a 2D space-time, yields black hole solutions, a plethora of new configurations have been obtained. These solutions turn out to admit both black hole (or black string)1−6) and cosmological interpretations7−11). In this letter I will consider a new conformal field theory on the world sheet, which can be understood as a diagonal Bianchi I cosmology. It turns out to be a closed, anisotropic universe, which recollapses after existing only a finite time, much like the recently constructed example of Nappi and Witten. They have found a closed recollapsing universe constructed as a conformal field theory on the coset SU(1, 1) × SU(2)/R and investigated its singularity structure. However, this solution is free of curvature singularities, as its global structure is that of a S × R anti-de-Sitter space-time crossed with a flat direction R . It is plagued with singularities in its causal structure, as closed timelike loops exist in it. It represents an extremal case of the gauged WZWN model on the coset SU(1, 1) × R/R and some internal conformal theory, where gauging is performed with taking the limit of the coupling of one of the free bosons to ∞ and keeping the other decoupled. This in effect decouples the SU(1, 1) group, too. Such extremal limit corresponds to the one discussed by Horne and Horowitz in relation to extremal black strings in 3D . A peculiarity of the solution is the constant dilaton, whose evolution is suppresed by a cancelation between the Kalb-Ramond charge and the effective cosmological constant, resulting from the central charge deficit. The action defining the effective field theory on the target space is, in the world sheet 2