Discrete Spectrum of the Graviton in the $AdS^5$ Black Hole Background

TL;DR

This paper calculates the discrete spectrum of graviton fluctuations in an AdS5 black hole background, revealing new mass relations and degeneracies among glueball states in a dual Yang-Mills theory.

Contribution

It provides the first detailed analysis of the graviton spectrum in this background, uncovering novel mass hierarchies and degeneracies among glueball states.

Findings

Ground state mass relation: $m(0^{++}) < m(2^{++}) < m(1^{-+})$

Discovered the $0^{++}$ graviton state has a smaller mass than the dilaton $0^{++}$

Variational methods yield accurate low-lying mass estimates; WKB describes higher modes

Abstract

The discrete spectrum of fluctuations of the metric about an $AdS^5$ black hole background are found. These modes are the strong coupling limit of so called glueball states in a dual 3-d Yang-Mills theory with quantum numbers $J^{PC} = 2^{++}, 1^{-+}, 0^{++}$. For the ground state modes, we find the mass relation: $m(0^{++}) < m(2^{++}) < m(1^{-+})$. Contrary to expectation, the mass of our new $0^{++}$ state ($m^2=5.4573$) associated with the graviton is smaller than the mass of the $0^{++}$ state ($m^2=11.588$) from the dilaton. In fact the dilatonic excitations are exactly degenerate with our tensor $2^{++}$ states. We find that variational methods gives remarkably accurate mass estimates for all three low-lying levels while a WKB treatment describes the higher modes well.