On the Classification of Spatially Homogeneous String Backgrounds

TL;DR

This paper classifies all spatially homogeneous 4D string backgrounds by extending Bianchi types, identifying 576 models including all FRW models, and discusses their physical significance within string theory.

Contribution

It provides a comprehensive classification of 4D string backgrounds based on Bianchi types, including a subset of 192 models with cosmological relevance.

Findings

Classified 576 spatially homogeneous string backgrounds.

Identified 192 models with FRW and asymptotic SO(3) isotropy.

Connected classification results with existing literature and string theory features.

Abstract

A classification of all possible spatially homogeneous 4D string backgrounds (HSBs) has been obtained by appropriate ramification of the existing nine Bianchi types of homogeneous 3D spaces. A total of $24^2=576$ HSBs which have been classified as distinct contains a subclass of 192 which includes all possible FRW models as well as those in which SO(3) isotropy is attained asymptotically. A discussion of these results also aims to fascilitate the identification of HSBs which have already appeared in the literature. The basic physical perspective of the parameters of classification is outlined together with certain features relating to deeper aspects of string theory.