Background independent holographic description : From matrix field theory to quantum gravity

TL;DR

This paper introduces a background independent holographic framework derived from matrix field theories, establishing a connection to quantum gravity with local spacetime transformations generated by RG procedures.

Contribution

It presents a novel local RG scheme that leads to background independent holographic duals, linking matrix field theories to (D+1)-dimensional quantum gravity.

Findings

Holographic duals are (D+1)-dimensional quantum gravity theories.

The gravitational theory exhibits (D+1) first-class constraints.

Diffeomorphism invariance arises from local RG scheme choices.

Abstract

We propose a local renormalization group procedure where length scale is changed in spacetime dependent way. Combining this scheme with an earlier observation that high energy modes in renormalization group play the role of dynamical sources for low energy modes at each scale, we provide a prescription to derive background independent holographic duals for field theories. From a first principle construction, it is shown that the holographic theory dual to a D-dimensional matrix field theory is a (D+1)-dimensional quantum theory of gravity coupled with matter fields of various spins. The gravitational theory has (D+1) first-class constraints which generate local spacetime transformations in the bulk. The (D+1)-dimensional diffeomorphism invariance is a consequence of the freedom to choose different local RG schemes.