Compromise of Localized Graviton with a Small Cosmological Constant in Randall-Sundrum Scenario

TL;DR

This paper introduces a new mechanism in the Randall-Sundrum scenario that localizes a massless graviton on the brane using boundary conditions, supported by analytical propagator solutions and path-integral techniques.

Contribution

It presents an analytical family of graviton propagators in AdS/CFT with boundary condition dependence, showing how a massless graviton can emerge via coupling renormalization.

Findings

Localized massless graviton achieved with Dirichlet boundary condition

Analytical propagator family parametrized by boundary conditions

Supports the view of Randall-Sundrum as a regularized underlying theory

Abstract

A new mechanism which leads to a linearized massless graviton localized on the brane is found in the $AdS$/CFT setting, {\it i.e.} in a single copy of $AdS_5$ spacetime with a singular brane on the boundary, within the Randall-Sundrum brane-world scenario. With an help of a recent development in path-integral techniques, a one-parameter family of propagators for linearized gravity is obtained analytically, in which a parameter $\xi$ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition ($\xi = 0$) the graviton localized on the brane can be massless {\it via} coupling constant renormalization. Our result supports a conjecture that the usual Randall-Sundrum scenario is a regularized version of a certain underlying theory.