Renormalization Group Flows from Gravity in Anti-de Sitter Space versus Black Hole No-Hair Theorems

Details Renormalization Group Flows from Gravity in Anti-de Sitter Space versus Black Hole No-Hair Theorems Renormalization Group Flows from Gravity in Anti-de Sitter Space versus Black Hole No-Hair Theorems

2000-03-06

arxiv.org/abs/hep-th/0003042v2

JHEP 0004 (2000) 011

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, 3 figures, harvmac, epsf, references and comments added

Scientific paper

10.1088/1126-6708/2000/04/011

Black hole no-hair theorems are proven using inequalities that govern the radial dependence of spherically symmetric configurations of matter fields. In this paper, we analyze the analogous inequalities for geometries dual to renormalization group flows via the AdS/CFT correspondence. These inequalities give much useful information about the qualitative properties of such flows. For Poincare invariant flows, we show that generic flows of relevant or irrelevant operators lead to singular geometries. For the case of irrelevant operators, this leads to an apparent conflict with Polchinski's decoupling theorem, and we offer two possible resolutions to this problem.

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