Stringy Resolutions of Null Singularities

TL;DR

This paper investigates null singularities in supersymmetric string theory backgrounds, showing that many such singularities are resolved by stringy effects like worldsheet instantons, leading to stable solutions despite classical singularities.

Contribution

It demonstrates that string theory can resolve null singularities through $\alpha'$-corrections, providing stable solutions even when classical geometries are singular.

Findings

Null singularities can be viewed as solutions to lower-dimensional Euclidean gravity.

Many null singularities are resolved by worldsheet instantons in string theory.

Resolved solutions remain stable despite classical singularities.

Abstract

We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form of the metric. As a result, the local nature of any such spacetime can be easily understood. We show that we can view any such geometry as a sequence of solutions to lower-dimensional Euclidean gravity. If we choose the lower-dimensional solutions to degenerate at some light-cone time, we obtain null singularities, which may be thought of as generalizations of the parabolic orbifold singularity. We find that in string theory, many such null singularities get repaired by $\alpha'$-corrections - in particular, by worldsheet instantons. As a consequence, the resulting string theory solutions do not suffer from any instability. Even though the CFT description of these solutions is not always valid, they can still be well understood after taking the effects of light D-branes into account; the breakdown of the worldsheet conformal field theory is purely gauge-theoretic, not involving strong gravitational effects.