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

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.

39 pages, 6 figures, uses JHEP3.cls, references added

References in corpus (3)

• Phase Diagram of N=4 Super-Yang-Mills Theory with R-Symmetry Chemical Potentials
• Blackhole/String Transition for the Small Schwarzschild Blackhole of $Ad{S}_5\times S^5$ and Critical Unitary Matrix Models
• Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3

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