Quantum gravity is investigated in the limit of a large number of space-time
dimensions, 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 $k_c/łambda=1/d$ (with $k=1/8
G$) 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 $| (k_c - k) |^1/2$, implying for the universal
gravitational critical exponent the value $\nu=0$ at $d=ınfty$.
%0 Generic
%1 citeulike:422894
%A Hamber, Herbert W.
%A Williams, Ruth M.
%D 2005
%K gravity quantum
%T Quantum Gravity in Large Dimensions
%U http://arxiv.org/abs/hep-th/0512003
%X Quantum gravity is investigated in the limit of a large number of space-time
dimensions, 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 $k_c/łambda=1/d$ (with $k=1/8
G$) 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 $| (k_c - k) |^1/2$, implying for the universal
gravitational critical exponent the value $\nu=0$ at $d=ınfty$.
@misc{citeulike:422894,
abstract = {Quantum gravity is investigated in the limit of a large number of space-time
dimensions, 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 $k_c/\lambda=1/d$ (with $k=1/8
\pi G$) 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 $| \log (k_c - k) |^{1/2}$, implying for the universal
gravitational critical exponent the value $\nu=0$ at $d=\infty$.},
added-at = {2007-08-18T13:22:24.000+0200},
author = {Hamber, Herbert W. and Williams, Ruth M.},
biburl = {https://www.bibsonomy.org/bibtex/2777e39a1c6156097b7996f663e70ab76/a_olympia},
citeulike-article-id = {422894},
description = {citeulike},
eprint = {hep-th/0512003},
interhash = {8aeb29753700542cd365e852df64329d},
intrahash = {777e39a1c6156097b7996f663e70ab76},
keywords = {gravity quantum},
month = Nov,
priority = {2},
timestamp = {2007-08-18T13:22:37.000+0200},
title = {Quantum Gravity in Large Dimensions},
url = {http://arxiv.org/abs/hep-th/0512003},
year = 2005
}