Quantum Gravity in Large Dimensions

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 $2d^2$ 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 $d=\infty$.

arXiv comment47 pages, 2 figures

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Cited by in corpus (20)

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• Fixed Points of Quantum Gravity and the Renormalisation Group
• Gravitational Wilson Loop and Large Scale Curvature
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• Inconsistencies from a Running Cosmological Constant
• The large D limit of dimensionally continued gravity
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• The Cosmology of an Infinite Dimensional Universe
• Gravitational Fluctuations as an Alternative to Inflation
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• TeV-scale gravity in Horava-Witten theory on a compact complex hyperbolic threefold
• Small black holes in the large D limit