Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm

TL;DR

This paper develops a holographic Wilsonian RG framework that connects integrating out high energy modes in field theories to removing parts of the bulk geometry in gravity duals, refining the black hole membrane paradigm.

Contribution

It introduces a method to perform Wilsonian RG in holography by geometrically integrating out bulk regions, providing new insights into low energy effective theories and the membrane paradigm.

Findings

Formulated a holographic Wilsonian RG procedure.

Connected bulk geometry integration to low energy effective theories.

Derived a semi-holographic description of low energy physics.

Abstract

We formulate a holographic Wilsonian renormalization group flow for strongly coupled systems with a gravity dual, motivated by the need to extract efficiently low energy behavior of such systems. Starting with field theories defined on a cut-off surface in a bulk spacetime, we propose that integrating out high energy modes in the field theory should correspond to integrating out a part of the bulk geometry. We describe how to carry out this procedure in practice in the classical gravity approximation using examples of scalar and vector fields. By integrating out bulk degrees of freedom all the way to a black hole horizon, this formulation defines a refined version of the black hole membrane paradigm. Furthermore, it also provides a derivation of the semi-holographic description of low energy physics.