Nonperturbative simplicial quantum gravity

Abstract

First results are presented for a discrete model of quantum gravity in two and four dimensions. The theory is defined on a simplicial lattice with the topology of a torus, and the edge lengths are taken as elementary variables. The problems of indefiniteness and non-renormalizability of the euclidean Einstein action are cured by adding cosmological constant and higher derivative terms, which are shown to be essential for approaching the lattice continuum limit. The theory is quantized using the stochastic method. The numerical results indicate that at strong coupling the average curvature is negative. A procedure for computing the renormalized, effective low energy, cosmological constant is outlined.