Black hole spectra in holography: consequences for equilibration of dual gauge theories

TL;DR

This paper investigates the spectrum of black holes in a specific holographic model, showing no energy gap exists, which implies that low-energy states can equilibrate through small black hole formation in the dual gauge theory.

Contribution

It provides a detailed analysis of black hole spectra in Pilch-Warner geometry, revealing the absence of an energy gap and implications for equilibration in the dual gauge theory.

Findings

No energy gap in black hole spectrum

Low-energy states can equilibrate via small black holes

Contrasts with models having non-equal central charges

Abstract

For a closed system to equilibrate from a given initial condition there must exist an equilibrium state with the energy equal to the initial one. Equilibrium states of a strongly coupled gauge theory with a gravitational holographic dual are represented by black holes. We study the spectrum of black holes in Pilch-Warner geometry. These black holes are holographically dual to equilibrium states of strongly coupled $SU(N)$ ${\cal N}=2^*$ gauge theory plasma on $S^3$ in the planar limit. We find that there is no energy gap in the black hole spectrum. Thus, there is a priory no obstruction for equilibration of arbitrary low-energy states in the theory via a small black hole gravitational collapse. The latter is contrasted with phenomenological examples of holography with dual four-dimensional CFTs having non-equal central charges in the stress-energy tensor trace anomaly.