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

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 $Σ_g\times\RrR$ with $Σ_g$ 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.