Non-perturbative summation over 3D discrete topologies

TL;DR

This paper develops a group field theory that non-perturbatively sums over all 3D topologies in discrete gravity, demonstrating its Borel summability and providing a new way to include all topologies in quantum gravity models.

Contribution

It introduces a unique Borel summable group field theory that sums over all 3D topologies in discrete gravity non-perturbatively.

Findings

Proves the theory is uniquely Borel summable.

Defines a non-perturbative sum over all triangulations and topologies.

Provides a framework for including all topologies in 3D quantum gravity.

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.