Non-commutative quantum geometric data in group field theories

Understand

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.