Strings in Time-Dependent Orbifolds

TL;DR

This paper investigates the conditions under which time-dependent orbifolds are suitable for perturbative string theory, analyzing their amplitudes and divergences, and identifying cases where perturbation theory is or isn't valid.

Contribution

It formulates criteria for perturbative analysis of time-dependent orbifolds and classifies low-dimensional cases, highlighting issues with certain geometries due to divergences.

Findings

Tree amplitudes show new infrared divergences from ultraviolet effects.

Three-dimensional parabolic orbifold is not suitable for perturbation theory.

Higher-dimensional backgrounds with enough noncompact dimensions are perturbatively consistent.

Abstract

We continue and extend our earlier investigation ``Strings in a Time-Dependent Orbifold'' (hep-th/0204168). We formulate conditions for an orbifold to be amenable to perturbative string analysis and classify the low dimensional orbifolds satisfying these conditions. We analyze the tree and torus amplitudes of some of these orbifolds. The tree amplitudes exhibit a new kind of infrared divergences which are a result of some ultraviolet effects. These UV enhanced IR divergences can be interpreted as due to back reaction of the geometry. We argue that for this reason the three dimensional parabolic orbifold is not amenable to perturbation theory. Similarly, the smooth four dimensional null-brane tensored with sufficiently few noncompact dimensions also appears problematic. However, when the number of noncompact dimensions is sufficiently large perturbation theory in these time dependent backgrounds seems consistent.