Quantum gravity in large dimensions

Herbert W. Hamber and Ruth M. Williams
Phys. Rev. D 73, 044031 – Published 24 February 2006

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 kc/λ=1/d (with k=1/8πG) separating a weak coupling from a strong coupling phase, and with 2d2 degenerate zero modes at kc. 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 |log(kck)|1/2, implying for the universal gravitational critical exponent the value ν=0 at d=.

  • Figure
  • Figure
  • Received 1 December 2005

DOI:https://doi.org/10.1103/PhysRevD.73.044031

©2006 American Physical Society

Authors & Affiliations

Herbert W. Hamber*

  • Department of Physics and Astronomy, University of California, Irvine, California 92697-4575, USA

Ruth M. Williams

  • Girton College, Cambridge CB3 0JG, United Kingdom
  • and Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

  • *Electronic address: HHamber@uci.edu
  • Electronic address: R.M.Williams@damtp.cam.ac.uk

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Issue

Vol. 73, Iss. 4 — 15 February 2006

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