Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1088/1126-6708/2007/01/001
Keywords
black holes in string theory; AdS-CFT correspondence; 1/N expansion; gauge-gravity correspondence
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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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