Exact Primordial Black Strings in Four Dimensions

TL;DR

This paper presents an exact four-dimensional solution in string theory describing a rotating black cosmic string, highlighting the role of the axion field and its relation to a WZWN sigma model.

Contribution

It introduces a novel exact solution in string theory representing a rotating black cosmic string with an axion field, constructed from a 3D black hole extended with a flat dimension.

Findings

The solution admits a rotating black cosmic string interpretation.

The axion acts similarly to a Higgs field in the model.

The solution is an exact WZWN sigma model to all orders in alpha'.

Abstract

A solution of effective string theory in four dimensions is presented which admits interpretation of a rotating black cosmic string. It is constructed by tensoring the three dimensional black hole, extended with the Kalb-Ramond axion, with a flat direction. The physical interpretation of the solution is discussed, with special attention on the axion, which is found to play a role very similar to a Higgs field. Finally, it is pointed out that the solution represents an exact WZWN $\sigma$ model on the string world sheet, to all orders in the inverse string tension $\alpha'$.