Is Quantum Gravity a Chern-Simons Theory?

TL;DR

This paper introduces a novel quantum gravity model using BV quantization of a supersymmetric matrix model, formulated as a Chern-Simons theory with potential for better UV behavior and a sum over causal structures.

Contribution

It presents a new quantum gravity framework based on an AKSZ-type Chern-Simons theory derived from a supersymmetric matrix model, expanding the approach to quantum gravity.

Findings

The model is formulated as a flat connection condition with zero curvature.

It sums over Hamiltonians associated with conformal classes of metrics.

The approach may improve ultraviolet behavior of quantum gravity theories.

Abstract

We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert space H. The model is motivated by previous attempts to formulate gravity in terms of non-commutative, phase space, field theories as well as the Fefferman-Graham curved analog of Dirac spaces for conformally invariant wave equations. The field equations are flat connection conditions amounting to zero curvature and parallel conditions on operators acting on H. This matrix-type model may give a better defined setting for a quantum gravity path integral. We demonstrate that its underlying physics is a summation over Hamiltonians labeled by a conformal class of metrics and thus a sum over causal structures. This gives in turn a model summing over fluctuating metrics plus a tower of additional modes-we speculate that these could yield improved UV behavior.