AdS/CFT and Randall-Sundrum Model Without a Brane

TL;DR

This paper reformulates the Randall-Sundrum model within AdS space by adding a boundary term, allowing gravity localization without branes and clarifying the connection to AdS/CFT correspondence.

Contribution

It introduces a boundary term in the AdS action to localize gravity without branes, linking RS and AdS/CFT frameworks more clearly.

Findings

Gravity can be localized on the boundary without branes.

Boundary conditions derive from field equations, not imposed.

Normalizable modes confirmed via inner product.

Abstract

We reformulate the Randall-Sundrum (RS) model on the compactified AdS by adding a term proportional to the area of the boundary to the usual gravity action with a negative cosmological constant and show that gravity can still be localized on the boundary without introducing singular brane sources. The boundary conditions now follow from the field equations, which are obtained by letting the induced metric vary on the boundary. This approach gives similar modes that are obtained in [1] and clarifies the complementarity of the RS and the AdS/CFT pictures. Normalizability of these modes is checked by an inner-product in the space of linearized perturbations. The same conclusions hold for a massless scalar field in the bulk.