Discrete spectrum of the graviton in the AdS5 black hole background

Abstract

The discrete spectrum of fluctuations of the metric about an AdS5 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 JPC=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 (m2=5.4573) associated with the graviton is smaller than the mass of the 0++ state (m2=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.