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Localised Gravity in the Singular Domain Wall Background?

M. Cvetic, H. Lu, C. N. Pope

TL;DR

The paper investigates localised gravity on singular AdS domain walls supported by the massive breathing-mode scalar from sphere reductions, revealing a well-defined fluctuation spectrum despite naked singularities. By formulating the problem as a Schrödinger equation with a potential that diverges negatively at the singularity yet remains bounded below, the authors show that a massless graviton is not bound in the unregularised setup, though a string-scale regularisation can produce exactly one massless bound state. They contrast this with domain walls from massless scalars, finding a shared spectral structure across different higher-dimensional origins. They also provide a higher-dimensional interpretation by oxidising to p-brane interiors, arguing that the inside-horizon regions may be physically relevant and potentially resolvable by stringy effects, analogous to negative-tension brane resolutions.

Abstract

We study singular, supersymmetric domain-wall solutions supported by the massive breathing mode scalars of, for example, sphere reductions in M-theory or string theory. The space-time on one side of such a wall is asymptotic to the Cauchy horizon of the anti-de Sitter (AdS) space-time. However, on the other side there is a naked singularity. The higher-dimensional embedding of these solutions has the novel interpretation of (sphere compactified) brane configurations in the domain ``inside the horizon region,'' with the singularity corresponding to the sphere shrinking to zero volume. The naked singularity is the source of an infinite attractive gravitational potential for the fluctuating modes. Nevertheless, the spectrum is bounded from below, continuous and positive definite, with the wave functions suppressed in the region close to the singularity. The massless bound state is formally excluded due to the boundary condition for the fluctuating mode wave functions at the naked singularity. However, a regularisation of the naked singularity, for example by effects of the order of the inverse string scale, in turn regularises the gravitational potential and allows for precisely one (massless) bound-state spin-2 fluctuating mode. We also contrast spectra in these domain wall backgrounds with those of the domain walls due to the massless modes of sphere reductions.

Localised Gravity in the Singular Domain Wall Background?

TL;DR

The paper investigates localised gravity on singular AdS domain walls supported by the massive breathing-mode scalar from sphere reductions, revealing a well-defined fluctuation spectrum despite naked singularities. By formulating the problem as a Schrödinger equation with a potential that diverges negatively at the singularity yet remains bounded below, the authors show that a massless graviton is not bound in the unregularised setup, though a string-scale regularisation can produce exactly one massless bound state. They contrast this with domain walls from massless scalars, finding a shared spectral structure across different higher-dimensional origins. They also provide a higher-dimensional interpretation by oxidising to p-brane interiors, arguing that the inside-horizon regions may be physically relevant and potentially resolvable by stringy effects, analogous to negative-tension brane resolutions.

Abstract

We study singular, supersymmetric domain-wall solutions supported by the massive breathing mode scalars of, for example, sphere reductions in M-theory or string theory. The space-time on one side of such a wall is asymptotic to the Cauchy horizon of the anti-de Sitter (AdS) space-time. However, on the other side there is a naked singularity. The higher-dimensional embedding of these solutions has the novel interpretation of (sphere compactified) brane configurations in the domain ``inside the horizon region,'' with the singularity corresponding to the sphere shrinking to zero volume. The naked singularity is the source of an infinite attractive gravitational potential for the fluctuating modes. Nevertheless, the spectrum is bounded from below, continuous and positive definite, with the wave functions suppressed in the region close to the singularity. The massless bound state is formally excluded due to the boundary condition for the fluctuating mode wave functions at the naked singularity. However, a regularisation of the naked singularity, for example by effects of the order of the inverse string scale, in turn regularises the gravitational potential and allows for precisely one (massless) bound-state spin-2 fluctuating mode. We also contrast spectra in these domain wall backgrounds with those of the domain walls due to the massless modes of sphere reductions.

Paper Structure

This paper contains 6 sections, 21 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Singular domain wall of the breathing mode
  3. Spectrum of fluctuating modes
  4. Regularising the metric near the naked singularity
  5. Singular domain walls with "massless" scalars
  6. Higher dimensional interpretation

Figures (2)

  • Figure 1: A sketch of the Schrödinger potential $V(z)$ as a function of $z$.
  • Figure 2: A sketch of the regularised Schrödinger potential $V(z)$ as a function of $z$. The negative infinity is cut-off at distances $z\sim -M^{-1}_{string}$ and at $z\ge 0$ a large barrier of order $M_{string}^2$ introduced.