On Smooth Time-Dependent Orbifolds and Null Singularities

TL;DR

This paper investigates string theory on a smooth, time-dependent orbifold called the null-brane, analyzing its geometry, string quantization, and potential resolution of singularities, providing insights into non-singular cosmological models in string theory.

Contribution

It introduces a non-singular time-dependent orbifold model, the null-brane, and explores its geometric properties, string quantization, and mechanisms for resolving singularities.

Findings

Backreaction due to test particles can be minimized.

String interactions on the smooth orbifold are nonsingular at tree level.

Physical modes may resolve the singularity in the orbifold.

Abstract

We study string theory on a non-singular time-dependent orbifold of flat space, known as the `null-brane'. The orbifold group, which involves only space-like identifications, is obtained by a combined action of a null Lorentz transformation and a constant shift in an extra direction. In the limit where the shift goes to zero, the geometry of this orbifold reproduces an orbifold with a light-like singularity, which was recently studied by Liu, Moore and Seiberg (hep-th/0204168). We find that the backreaction on the geometry due to a test particle can be made arbitrarily small, and that there are scattering processes which can be studied in the approximation of a constant background. We quantize strings on this orbifold and calculate the torus partition function. We construct a basis of states on the smooth orbifold whose tree level string interactions are nonsingular. We discuss the existence of physical modes in the singular orbifold which resolve the singularity. We also describe another way of making the singular orbifold smooth which involves a sandwich pp-wave.