Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions

TL;DR

This paper proves the renormalizability of a class of three-dimensional SU(2) tensorial group field theories, establishing a new framework for quantum gravity models with detailed technical classifications.

Contribution

It introduces a renormalizable SU(2) tensorial group field theory model in three dimensions, with a comprehensive classification of renormalizable interactions and graph properties.

Findings

Tensorial interactions up to degree 6 are renormalizable.

Provides a classification of renormalizable models with gauge invariance.

Analyzes properties of melonic graphs and wave-function renormalization.

Abstract

We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.