Quantum gravity in large dimensions

Abstract

Quantum gravity is investigated in the limit of a large number of space-time dimensions d, using as an ultraviolet regularization the simplicial lattice path integral formulation. In the weak field limit the appropriate expansion parameter is determined to be 1/d. For the case of a simplicial lattice dual to a hypercube, the critical point is found at k{sub c}/{lambda}=1/d (with k=1/8{pi}G) separating a weak coupling from a strong coupling phase, and with 2d{sup 2} degenerate zero modes at k{sub c}. The strong coupling, large G, phase is then investigated by analyzing the general structure of the strong coupling expansion in the large d limit. Dominant contributions to the curvature correlation functions are described by large closed random polygonal surfaces, for which excluded volume effects can be neglected at large d, and whose geometry we argue can be approximated by unconstrained random surfaces in this limit. In large dimensions the gravitational correlation length is then found to behave as vertical bar log(k{sub c}-k) vertical bar{sup 1/2}, implying for the universal gravitational critical exponent the value {nu}=0 at d={infinity}.