Multi-orientable Group Field Theory

TL;DR

This paper introduces multi-orientable GFT as a new simplification method for group field theories, analyzing its graph structures, properties, and potential for renormalization, extending from 3D to 4D models.

Contribution

It proposes multi-orientable GFT, explores its relation to colorable graphs, and discusses its topological and renormalization properties, including generalization to higher dimensions.

Findings

Absence of tadfaces and some generalized tadpoles in multi-orientable GFT graphs

Established relation between multi-orientable and colorable GFT graphs

Performed Feynman amplitude computations for the new model

Abstract

Group Field Theories (GFT) are quantum field theories over group manifolds; they can be seen as a generalization of matrix models. GFT Feynman graphs are tensor graphs generalizing ribbon graphs (or combinatorial maps); these graphs are dual not only to manifolds. In order to simplify the topological structure of these various singularities, colored GFT was recently introduced and intensively studied since. We propose here a different simplification of GFT, which we call multi-orientable GFT. We study the relation between multi-orientable GFT Feynman graphs and colorable graphs. We prove that tadfaces and some generalized tadpoles are absent. Some Feynman amplitude computations are performed. A few remarks on the renormalizability of both multi-orientable and colorable GFT are made. A generalization from three-dimensional to four-dimensional theories is also proposed.