Lost in Translation: Topological Singularities in Group Field Theory

TL;DR

This paper investigates the topological properties of Group Field Theory graphs, revealing that while some graphs are not pseudo manifolds, colored GFT models exclusively generate graphs dual to pseudo manifolds across all dimensions.

Contribution

It proves that uncolored GFT graphs can fail to be pseudo manifolds in higher dimensions, but colored GFT models avoid this issue, ensuring topological consistency.

Findings

Uncolored GFT graphs can be non-pseudo manifolds in higher dimensions.

Colored GFT models only produce graphs dual to pseudo manifolds.

Topological singularities are present in certain GFT graphs.

Abstract

Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs are dual to gluings of higher dimensional simplices. It is generally assumed that GFT graphs are always dual to pseudo manifolds. In this paper we prove that already in dimension three (and in all higher dimensions), this is not true due to subtle differences between simplicial complexes and gluings dual to GFT graphs. We prove however that, fortunately, the recently introduced "colored" GFT models [1] do not suffer from this problem and only generate graphs dual to pseudo manifolds in any dimension.