Non-perturbative summation over 3D discrete topologies

Abstract

We construct a group field theory which realizes the sum of gravity amplitudes over all three dimensional topologies trough a perturbative expansion. We prove this theory to be uniquely Borel summable. This shows how to define a non-perturbative summation over triangulations including all topologies in the context of three dimensional discrete gravity.

20 pages, 9 figures, note added, minor corrections

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