Supergravity on the Brane

TL;DR

This work constructs a fully non-linear brane-world scenario by embedding a thick domain wall in AdS and superposing a non-linear pp-wave, obtaining a single graviton bound state on the brane akin to Randall-Sundrum. It shows that a first-order Bogomolnyi flow can yield thick-domain-wall solutions and that a z-independent m^2 = 0 mode reproduces the RS bound state in a non-linear setting, with possible partial supersymmetry. The analysis of bulk waves in Siklos coordinates reveals that generic waves drive pp curvature singularities at the AdS horizon, though brane physics may be red-shifted and potentially unaffected. The paper also highlights the challenge of deriving a suitable superpotential from supergravity in these setups, marking an open problem for embedding RS-like scenarios into a consistent non-linear framework.

Abstract

We show that smooth domain wall spacetimes supported by a scalar field separating two anti-de-Sitter like regions admit a single graviton bound state. Our analysis yields a fully non-linear supergravity treatment of the Randall-Sundrum model. Our solutions describe a pp-wave propagating in the domain wall background spacetime. If the latter is BPS, our solutions retain some supersymmetry. Nevertheless, the Kaluza-Klein modes generate ``pp curvature'' singularities in the bulk located where the horizon of AdS would ordinarily be.