Quantum Renormalization Group and Holography

TL;DR

This paper explores how quantum renormalization group techniques elucidate the emergence of Einstein gravity in holography, linking beta functions of quantum field theories to bulk gravitational actions.

Contribution

It demonstrates that Einstein gravity arises as a long-wavelength holographic description of matrix field theories with specific operator spectra and reveals symmetry properties of holographic actions related to beta function flows.

Findings

Einstein gravity emerges from matrix field theories with only the energy-momentum tensor as a finite scaling dimension operator.

Holographic actions respect inversion symmetry if beta functions are gradient flows.

The work establishes a microscopic link between quantum RG and holographic duality.

Abstract

Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the Einstein gravity emerges as a long wavelength holographic description for a matrix field theory which has no other operator with finite scaling dimension except for the energy-momentum tensor. We also point out that holographic actions for general large N matrix field theories respect the inversion symmetry along the radial direction in the bulk if the beta functions of single-trace operators are gradient flows with respect to the target space metric set by the beta functions of double-trace operators.