A power law for the lowest eigenvalue in localized massive gravity

TL;DR

The paper investigates the localization of a massive graviton on a four-dimensional AdS brane within a five-dimensional warped geometry. By factorizing the fluctuation operator into supersymmetric partner Hamiltonians H1 and H2, it reduces the problem to the odd sector of H1 and solves the resulting Schrödinger-like equation using hypergeometric functions, with eigenvalues determined by boundary conditions. A key result is the explicit quadratic dependence of the lowest eigenvalue on the small parameter beta: E0(beta) = (3/2) beta^2 + O(beta^4), which translates into a quadratic scaling m0^2 ~ (3/2) |Lambda|^2 x0^2 for the physical parameters. This contrasts with a naive linear scaling expected from scaling arguments and clarifies how localization and parity structure shape the graviton spectrum in localized massive gravity models.

Abstract

This short note contains a detailed analysis to find the right power law the lowest eigenvalue of a localized massive graviton bound state in a four dimensional AdS background has to satisfy. In contrast to a linear dependence of the cosmological constant we find a quadratic one [hep-th/0011156].