Holographic renormalisation group ows and renormalisation from a Wilsonian perspective

Abstract

From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular xed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satis ed by the Wilson action and nd the corresponding xed points and their eigendeformations, which have a diagonal evolution close to the xed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss di erent renormalisation schemes and show that the solutions to the gravity equations of motion can be used as renormalised couplings that parametrise the renormalised theories. This provides a transparent connection between holographic renormalisation group ows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space.