Instabilities of the Small Black Hole: a view from N=4 SYM

TL;DR

This paper analyzes the stability of small black holes in N=4 SYM at finite temperature, revealing a weak coupling instability analogous to the Gregory-Laflamme instability in gravity, with implications for black hole decay.

Contribution

It introduces a one-loop effective potential for N=4 SYM that captures the weak coupling instability analogous to gravitational Gregory-Laflamme instability.

Findings

Effective potential develops unstable directions above a critical temperature.

Identifies weak coupling instability as the field theory counterpart of gravitational localization.

Provides a holographic description of black hole decay processes.

Abstract

We compute a one-loop effective action for the constant modes of the scalars and the Polyakov loop matrix of N=4 SYM on S^3 at finite temperature and weak 't Hooft coupling. Above a critical temperature, the effective potential develops new unstable directions accompanied by new saddle points which only preserve an SO(5) subgroup of the SO(6) global R-symmetry. We identify this phenomenon as the weak coupling version of the well known Gregory-Laflamme localization instability in the gravity dual of the strongly coupled field theory: The small AdS_5 black hole when viewed as a ten dimensional, asymptotically AdS_5 X S^5 solution smeared on the S^5 is unstable to localization on S^5. Our effective potential, in a specific Lorentzian continuation, can provide a qualitative holographic description of the decay of the "topological black hole'' into the AdS bubble of nothing.