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

Vatche Sahakian
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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.

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Vatche Sahakian. 1999-10-15. Holography, a covariant c-function, and the geometry of the renormalization group. https://doi.org/10.1103/physrevd.62.126011

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