Holographic renormalisation group flows and renormalisation from a Wilsonian perspective

TL;DR

This paper explores the connection between Wilsonian renormalisation group flows and holographic duality, demonstrating how fixed points and deformations in gravity correspond to renormalised theories, with explicit scalar field examples in AdS.

Contribution

It provides a detailed analysis of holographic renormalisation group flows from a Wilsonian perspective, linking Hamilton-Jacobi formalism with holographic renormalisation schemes.

Findings

Fixed points and eigendeformations identified in gravity duals.

Explicit scalar theory calculations in AdS illustrate the formalism.

Connections established between Wilsonian and holographic renormalisation approaches.

Abstract

From the Wilsonian point of view, renormalisable theories are understood as submanifolds in theory space emanating from a particular fixed point under renormalisation group evolution. We show how this picture precisely applies to their gravity duals. We investigate the Hamilton-Jacobi equation satisfied by the Wilson action and find the corresponding fixed points and their eigendeformations, which have a diagonal evolution close to the fixed points. The relevant eigendeformations are used to construct renormalised theories. We explore the relation of this formalism with holographic renormalisation. We also discuss different 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 flows in the Wilsonian and non-Wilsonian approaches. The general results are illustrated by explicit calculations in an interacting scalar theory in AdS space.