Group field theory renormalization - the 3d case: power counting of divergences

TL;DR

This paper advances the understanding of divergences in 3D Group Field Theory by developing a power counting method for a specific class of graphs, aiding the study of quantum spacetime emergence.

Contribution

It introduces an algorithm for boundary triangulation and establishes power counting for a class of graphs in 3D GFT, progressing towards quantum gravity insights.

Findings

Identified boundary structures of 3D GFT bubbles.

Developed a contraction procedure for a special graph class.

Proved power counting results for these graphs.

Abstract

We take the first steps in a systematic study of Group Field Theory renormalization, focusing on the Boulatov model for 3D quantum gravity. We define an algorithm for constructing the 2D triangulations that characterize the boundary of the 3D bubbles, where divergences are located, of an arbitrary 3D GFT Feynman diagram. We then identify a special class of graphs for which a complete contraction procedure is possible, and prove, for these, a complete power counting. These results represent important progress towards understanding the origin of the continuum and manifold-like appearance of quantum spacetime at low energies, and of its topology, in a GFT framework.