GEMs and amplitude bounds in the colored Boulatov model

TL;DR

This paper develops a methodology to analyze divergences in colored group field theory by using Graph-Encoded-Manifolds to separate topological contributions, with applications to 3D solid tori in the Boulatov model.

Contribution

It introduces a novel approach combining amplitude bounds and GEM techniques to factorize divergences related to different topologies in colored group field theories.

Findings

GEM techniques effectively separate topological divergences.

Amplitude bounds are established using propagator cuts.

Application demonstrated on 3D solid torus topologies.

Abstract

In this paper we construct a methodology for separating the divergencies due to different topological manifolds dual to Feynman graphs in colored group field theory. After having introduced the amplitude bounds using propagator cuts, we show how Graph-Encoded-Manifolds (GEM) techniques can be used in order to factorize divergencies related to different parts of the dual topologies of the Feynman graphs in the general case. We show the potential of the formalism in the case of 3-dimensional solid torii in the colored Boulatov model.