An Exact String Theory Model of Closed Time-Like Curves and Cosmological Singularities

TL;DR

This paper constructs an exact string theory model with closed time-like curves and cosmological singularities, analyzing string corrections and suggesting string theory can handle such exotic spacetime features.

Contribution

It provides a full conformal field theory embedding of Taub-NUT geometry with CTCs, including all alpha' corrections, offering insights into stringy resolutions of singularities and CTCs.

Findings

Persistence of Taub-NUT features in the exact theory

Emergence of Euclidean signature regions bounded by singularities

String theory may resolve or make sense of CTCs and singularities

Abstract

We study an exact model of string theory propagating in a space-time containing regions with closed time-like curves (CTCs) separated from a finite cosmological region bounded by a Big Bang and a Big Crunch. The model is an non-trivial embedding of the Taub-NUT geometry into heterotic string theory with a full conformal field theory (CFT) definition, discovered over a decade ago as a heterotic coset model. Having a CFT definition makes this an excellent laboratory for the study of the stringy fate of CTCs, the Taub cosmology, and the Milne/Misner-type chronology horizon which separates them. In an effort to uncover the role of stringy corrections to such geometries, we calculate the complete set of alpha' corrections to the geometry. We observe that the key features of Taub-NUT persist in the exact theory, together with the emergence of a region of space with Euclidean signature bounded by time-like curvature singularities. Although such remarks are premature, their persistence in the exact geometry is suggestive that string theory theory is able to make physical sense of the Milne/Misner singularities and the CTCs, despite their pathological character in General Relativity. This may also support the possibility that CTCs may be viable in some physical situations, and may be a natural ingredient in pre-Big-Bang cosmological scenarios.