Weyl Invariant Spacetime

TL;DR

This paper introduces a new class of Weyl invariant backgrounds in string theory, featuring a ten-dimensional spacetime composed of flat four-dimensional space and curved six-dimensional space with non-zero Ricci tensors, and monopole-type Kalb-Ramond fields.

Contribution

It presents novel Weyl invariant backgrounds with non-trivial Kalb-Ramond fields that are globally non-exact, expanding the understanding of consistent string backgrounds.

Findings

Spacetime is a product of flat 4D and curved 6D with Ricci curvature.

Kalb-Ramond fields are monopole type and globally non-exact.

Spacetime is homogeneous and free of singularities.

Abstract

A new class of Weyl invariant backgrounds are presented in terms of the metric $G_{\mu\nu}$ and the anti-symmetric Kalb-Ramond fields $B_{\mu\nu}$. The ten-dimensional spacetime is a product of four-dimensional flat spacetime and curved six-dimensional spacetime having nonvanishing Ricci tensors. The non-vanishing Kalb-Ramond field strengths cannot be written globally as $H=dB$, being of the monopole type. Nevertheless they define homogeneous spacetime with no singularity.