A simple proof of orientability in colored group field theory

TL;DR

This paper demonstrates that the presence of two interaction vertices in colored group field theories guarantees the orientability of the associated piecewise linear pseudo-manifolds, using crystallization theory.

Contribution

It provides a simple proof linking color and orientability in group field theories through crystallization results, clarifying the topological implications of coloring.

Findings

Color in group field theories ensures orientability of associated manifolds.

The proof relies on crystallization theory to establish orientability.

Presence of two interaction vertices is key to orientability.

Abstract

In this short note we use results from the theory of crystallizations to prove that color in group field theories garantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. The origin of orientability is the presence of two interaction vertices.