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

Timothy Hollowood·S. Prem Kumar·Asad Naqvi
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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.

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Timothy Hollowood, S. Prem Kumar, Asad Naqvi. 2006-10-11. Instabilities of the Small Black Hole: a view from N=4 SYM. https://doi.org/10.1088/1126-6708%2F2007%2F01%2F001

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