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

TL;DR

This paper introduces a covariant geometric c-function for theories with gravitational duals, proves a c-theorem, and applies it to various geometries, confirming consistency with theoretical expectations.

Contribution

It presents a new covariant geometric c-function, establishes a c-theorem for it, and demonstrates its applicability across multiple gravitational geometries.

Findings

The covariant c-function satisfies the c-theorem.

Application to various geometries shows agreement with theoretical expectations.

The approach unifies different geometries under a common c-function framework.

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.