Wheeler-DeWitt Equation in 2 + 1 Dimensions

TL;DR

This paper investigates the infrared properties of quantum gravity in 2+1 dimensions by solving lattice Wheeler-DeWitt equations, revealing a finite correlation length and supporting the existence of a non-perturbative ultraviolet fixed point.

Contribution

It provides an exact determination of the correlation length exponent and demonstrates the emergence of a finite correlation length that regularizes infrared divergences in 2+1 dimensional quantum gravity.

Findings

Finite correlation length emerges, cutting off infrared divergences.

Existence of an ultraviolet fixed point at zero G.

Correlation length exponent is exactly $ u=6/11$.

Abstract

The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wavefunction solutions is such that a finite correlation length emerges and naturally cuts off any infrared divergences. Properties of the lattice vacuum are consistent with the existence of an ultraviolet fixed point in $G$ located at the origin, thus precluding the existence of a weak coupling perturbative phase. The correlation length exponent is determined exactly and found to be $\nu=6/11$. The results obtained so far lend support to the claim that the Lorentzian and Euclidean formulations belong to the same field-theoretic universality class.