Covariant Holographic Renormalization of Non-Conformal Field Theories

Abstract

We present a Covariant Holographic Renormalization (CHR) procedure of fake supergravity (sugra) systems. Holography is a strong/weak coupling duality between gravitational and gauge theories, and fake sugra is a theory of gravity coupled to scalars in which the scalar potential can be derived from a superpotential in some specific way. Other systematic methods of holographic renormalization of fake sugra exist, but they are all restricted to spacetimes that are asymptotically anti-de Sitter (aAdS). According to the AdS/CFT correspondence, their dual quantum field theories are conformal in the ultraviolet. Covariant Holographic Renormalization can be applied to fake sugra systems in both aAdS and non-aAdS backgrounds. The field theories dual to non-aAdS sugra systems are non-conformal. So far, the method is limited to the renormalization of two-point functions. The CHR procedure shows that the divergences from the bare fake sugra action can be cancelled by covariant counterterms without introducing new divergences.