Space-time foam in 2D and the sum over topologies

Abstract

It is well-known that the sum over topologies in quantum gravity is ill-defined, due to a super-exponential growth of the number of geometries as a function of the space-time volume, leading to a badly divergent gravitational path integral. Not even in dimension 2, where a non-perturbative quantum gravity theory can be constructed explicitly from a (regularized) path integral, has this problem found a satisfactory solution. -- In the present work, we extend a previous 2d Lorentzian path integral, regulated in terms of Lorentzian random triangulations, to include space-times with an arbitrary number of handles. We show that after the imposition of physically motivated causality constraints, the combined sum over geometries and topologies is well-defined and possesses a continuum limit which yields a concrete model of space-time foam in two dimensions.

13 pages, 6 Postscript figures; contribution to the proceedings of the Workshop on Random Geometry, Krakow, May 15-17, 2003

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• The Universe from Scratch
• The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
• Taming the cosmological constant in 2D causal quantum gravity with topology change
• Gauge fixing in Causal Dynamical Triangulations
• A causal perspective on random geometry
• Gauge Group and Topology Change