Homogeneous Conformal String Backgrounds

TL;DR

This paper presents exact homogeneous string backgrounds with specific Bianchi-type metrics, highlighting the inevitability of curvature singularities and limitations of duality transformations in non-semisimple isometry groups.

Contribution

It provides explicit solutions for homogeneous string backgrounds and demonstrates the failure of standard duality methods in certain non-semisimple cases.

Findings

Curvature singularities are unavoidable in these backgrounds.

Standard duality transformations fail for non-semisimple isometry groups.

Flat spacetime with constant dilaton is the only exception.

Abstract

We present exact solutions characterised by Bianchi-type I,II,III,V,VI four-dimensional metric, space-independent dilaton, and vanishing torsion background, for the low energy string effective action with zero central charge deficit. We show that, in such a context, curvature singularities cannot be avoided, except for the trivial case of flat spacetime and constant dilaton. We also provide a further example of the failure of the standard prescription for connecting conformal string backgrounds through duality transformations associated to non-semisimple, non-Abelian isometry group.