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 wave function 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.

• Received 12 July 2012

DOI:https://doi.org/10.1103/PhysRevD.86.084010