Year: 2006
Type: article
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 ${k}_{c}/\ensuremath{\lambda}=1/d$ (with $k=1/8\ensuremath{\pi}G$) separating a weak coupling from a strong coupling phase, and with $2{d}^{2}$ degenerate zero modes at ${k}_{c}$. 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 $|\mathrm{log}({k}_{c}\ensuremath{-}k){|}^{1/2}$, implying for the universal gravitational critical exponent the value $\ensuremath{\nu}=0$ at $d=\ensuremath{\infty}$.
Authors: Herbert W. Hamber, Ruth M. Williams
Institutions: University of California, Irvine, University of Cambridge
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2145171744