Holography, a covariant c-function, and the geometry of the renormalization group

Abstract

We propose a covariant geometrical expression for the c-function for theories which admit dual gravitational descriptions. We state a c-theorem with respect to this quantity and prove it. We apply the expression to a class of geometries, from domain walls in gauged supergravities, to extremal and near extremal Dp branes, and the AdS Schwarzschild black hole. In all cases, we find agreement with expectations.

20 pages, 1 figure; minor clarifications, a reference added, and a few typos corrected

References in corpus (3)

• Gravitational Stability and Renormalization-Group Flow
• The Supergravity Dual of N=1 Super Yang-Mills Theory
• Proof of Classical Versions of the Bousso Entropy Bound and of the Generalized Second Law

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