Matrix Models as Non-commutative Field Theories on R^3

Understand

In the context of spin foam models for quantum gravity, group field theories are a useful tool allowing on the one hand a non-perturbative formulation of the partition function and on the other hand admitting an interpretation as generalized matrix models.

• Focusing on 2d group field theories, we review their explicit relation to matrix models and show their link to a class of non-commutative field theories invariant under a quantum deformed 3d Poincare symmetry.
• This provides a simple relation between matrix models and non-commutative geometry.
• Moreover, we review the derivation of effective 2d group field theories with non-trivial propagators from Boulatov's group field theory for 3d quantum gravity.