Spin-2 spectrum of defect theories

TL;DR

This paper analyzes spin-2 excitations in type-IIB supergravity solutions dual to defect conformal field theories, deriving their spectra and exploring implications for localized gravity and higher-dimensional embeddings.

Contribution

It generalizes the wave equation for spin-2 modes in these backgrounds and solves it numerically for the Janus solution, revealing how the spectrum varies with the dilaton jump.

Findings

Spectrum depends on the dilaton-jump parameter $\Delta\phi$

In large $\Delta\phi$ limit, geometry becomes effectively five-dimensional

Numerical solutions exhibit the behavior of spin-2 modes in defect backgrounds

Abstract

We study spin-2 excitations in the background of the recently-discovered type-IIB solutions of D'Hoker et al. These are holographically-dual to defect conformal field theories, and they are also of interest in the context of the Karch-Randall proposal for a string-theory embedding of localized gravity. We first generalize an argument by Csaki et al to show that for any solution with four-dimensional anti-de Sitter, Poincare or de Sitter invariance the spin-2 excitations obey the massless scalar wave equation in ten dimensions. For the interface solutions at hand this reduces to a Laplace-Beltrami equation on a Riemann surface with disk topology, and in the simplest case of the supersymmetric Janus solution it further reduces to an ordinary differential equation known as Heun's equation. We solve this equation numerically, and exhibit the spectrum as a function of the dilaton-jump parameter $\Delta\phi$. In the limit of large $\Delta\phi$ a nearly-flat linear-dilaton dimension grows large, and the Janus geometry becomes effectively five-dimensional. We also discuss the difficulties of localizing four-dimensional gravity in the more general backgrounds with NS5-brane or D5-brane charge, which will be analyzed in detail in a companion paper.