Unitarity and singular backgrounds

TL;DR

This paper analyzes the graviton spectrum in a gravity-dilaton background with a naked singularity, identifying conditions under which the spectrum is stable and contains a massless graviton mode.

Contribution

It applies quantum mechanics methods to determine boundary conditions that yield a stable, tachyon-free graviton spectrum in singular backgrounds.

Findings

Spectrum contains a tachyon for most boundary conditions.

A specific boundary condition yields a tachyon-free, stable spectrum.

The lowest graviton mode is massless under the stable boundary condition.

Abstract

We compute the graviton Kaluza-Klein spectrum on a gravity-dilaton background with a naked singularity for all possible boundary conditions at the singularity which are consistent with unitary evolution. We apply methods from non-relativistic quantum mechanics with singular Schr\"{o}dinger potentials. In general the spectrum contains a tachyon, a sign of instability. Only for a particular boundary condition at the singularity is the spectrum free of tachyons. In this case the lowest-lying graviton mode is massless. We argue that this result will also hold for other backgrounds with similar geometry near the curvature singularity. We complete our study with a brief discussion on radion perturbations and the Higgs mechanism on this singular background.