The Sum over Topologies in Three-Dimensional Euclidean Quantum Gravity

Abstract

In Hawking's Euclidean path integral approach to quantum gravity, the partition function is computed by summing contributions from all possible topologies. The behavior such a sum can be estimated in three spacetime dimensions in the limit of small cosmological constant. The sum over topologies diverges for either sign of $\Lambda$, but for dramatically different reasons: for $\Lambda >0$, the divergent behavior comes from the contributions of very low volume, topologically complex manifolds, while for $\Lambda <0$ it is a consequence of the existence of infinite sequences of relatively high volume manifolds with converging geometries. Possible implications for four-dimensional quantum gravity are discussed.

12 pages (LaTeX), UCD-92-16

References in corpus (1)

• Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave Function

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