Three dimensional lattice gravity as supersymmetric Yang-Mills theory

TL;DR

The paper proposes that a twisted supersymmetric Yang-Mills theory in three dimensions can serve as a non-perturbative framework for three-dimensional quantum gravity, linking topological observables to Chern-Simons theory.

Contribution

It introduces a novel connection between 3D supersymmetric Yang-Mills theory and quantum gravity via topological observables and discretization methods.

Findings

Topological observables in the YM theory relate to Chern-Simons theory.

Discretization preserves topological observable values.

Conjecture of YM theory as a non-perturbative quantum gravity definition.

Abstract

We argue that a certain twisted supersymmetric Yang-Mills theory in three dimensions with gauge group SU(2) possesses a set of topological observables whose expectation values can be computed in a related Chern Simons theory. This Chern Simons theory has been proposed as a definition of three dimensional Euclidean quantum gravity. Since the YM theory admits a discretization which preserves the values of topological observables we conjecture that it can be used as a non-perturbative definition of the quantum gravity theory.