2+1 Dimensional Quantum Gravity as a Gaussian Fermionic System and the 3D-Ising Model

TL;DR

This paper demonstrates that 2+1-dimensional Euclidean quantum gravity can be modeled as a Gaussian fermionic system and relates it to the 3D lattice Ising model, providing a new perspective on quantum gravity and statistical mechanics.

Contribution

It establishes an equivalence between 2+1D Euclidean quantum gravity and Gaussian fermionic systems, linking it to the 3D Ising model before the thermodynamic limit.

Findings

Quantum gravity in 2+1D can be represented as a Gaussian fermionic system.

The model relates to the 3D lattice Ising model on certain manifolds.

Provides a new approach to studying quantum gravity using statistical mechanics.

Abstract

We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under some mild topological assumptions, to a Gaussian fermionic system. In particular, for manifolds topologically equivalent to $\Sigma_g\times\RrR$ with $\Sigma_g$ a closed and oriented Riemann surface of genus $g$, the corresponding 2+1-dimensional Euclidean quantum gravity may be related to the 3D-lattice Ising model before its thermodynamic limit.