Noncompact nonlinear sigma models and numerical quantum gravity

Abstract

The O(2,1) nonlinear sigma model is a useful stepping stone toward determining whether or not a consistent quantum theory of gravity (based on the Einstein-Hilbert action) exists. Like gravity, the sigma model is not perturbatively renormalizable, and corresponding Feynman graphs in the two theories have the same naïve degrees of divergence. Both theories also have a single overall dimensionful coupling constant, and both have a configuration space which is noncompact and curved. The sigma model allows one to study the renormalizability properties of such theories without the added complications of local symmetries. We will report the latest results of lattice field theory simulations of the O(2,1) sigma model, the purpose of which is to determine if the model is nonperturbatively renormalizable. The implications for a quantum theory of gravity are also discussed.