Non-commutative quantum geometric data in group field theories

TL;DR

This paper reviews how group field theories incorporate non-commutative geometric data, connecting tensor models to quantum gravity and lattice gauge theories, highlighting the role of non-commutative flux representations.

Contribution

It provides a concise overview of the role of non-commutative flux data in group field theories and their relation to quantum gravity models.

Findings

GFT amplitudes resemble lattice gauge theories and simplicial gravity path integrals.

Non-commutative flux representation makes quantum geometry explicit.

Enhances understanding of geometric data in quantum gravity frameworks.

Abstract

We review briefly the motivations for introducing additional group-theoretic data in tensor models, leading to the richer framework of group field theories, themselves a field theory formulation of loop quantum gravity. We discuss how these data give to the GFT amplitudes the structure of lattice gauge theories and simplicial gravity path integrals, and make their quantum geometry manifest. We focus in particular on the non-commutative flux/algebra representation of these models.