Bubbles and jackets: new scaling bounds in topological group field theories

TL;DR

This paper introduces new scaling bounds for topological group field theories in 3 and 4 dimensions, improving understanding of their perturbative expansions and singularity suppression.

Contribution

It provides novel bubble and jacket bounds for Feynman amplitudes, enhancing the analysis of topological and tensorial group field theories.

Findings

Bubble bound shows suppression of singular topologies.

A stronger jacket bound is established.

Results are relevant for quantum gravity models.

Abstract

We use a reformulation of topological group field theories in 3 and 4 dimensions in terms of variables associated to vertices, in 3d, and edges, in 4d, to obtain new scaling bounds for their Feynman amplitudes. In both 3 and 4 dimensions, we obtain a bubble bound proving the suppression of singular topologies with respect to the first terms in the perturbative expansion (in the cut-off). We also prove a new, stronger jacket bound than the one currently available in the literature. We expect these results to be relevant for other tensorial field theories of this type, as well as for group field theory models for 4d quantum gravity.