Gravity Is Induced By Renormalization Group Flow

TL;DR

This paper demonstrates that gravity can emerge as an effective phenomenon from quantum effects in a 4d field theory via holographic renormalization group flow, linking quantum field theory deformations to dynamical spacetime backgrounds.

Contribution

It shows how Einstein gravity arises from quantum effects in a 4d field theory through holographic RG flow, suggesting gravity is an emergent, effective force rather than fundamental.

Findings

Quantum effects induce an effective 4d Einstein gravity from a non-gravitating theory.

Holographic RG flow relates field theory deformations to dynamical metrics.

Gravity emerges as an IR effective description in the holographic framework.

Abstract

We revisit the holographic renormalization group (RG) setting in which a 4-dimensional ($4d$) quantum field theory at a finite cutoff corresponds to/is described by the Einstein gravity on a part of AdS$_{5}$ space, cutoff at a finite radius. This holographic setting has interesting and important implications for the $4d$ field theory: Deformation of the field theory by a certain combination involving the square of its energy-momentum tensor can be alternatively viewed as formulating the field theory on a background with a dynamical metric. Explicitly, starting with a non-gravitating $4d$ field theory in the UV, flowing to the IR, quantum effects that we compute using the classical $5d$ Einstein gravity theory, induce an effective $4d$ Einstein gravity theory. In other words, we show that gravity is not a fundamental force and is an effective description of quantum effects in the IR limit.