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arXiv · hep-th/0309012

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

R. Loll·W. Westra
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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.

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R. Loll, W. Westra. 2003-08-31. Space-time foam in 2D and the sum over topologies. https://arxiv.org/abs/hep-th/0309012

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