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In the context of spin foam models for quantum gravity, group field theoriesare a useful tool allowing on the one hand a non-perturbative formulation ofthe partition function and on the other hand admitting an interpretation asgeneralized matrix models. Focusing on 2d group field theories, we review theirexplicit relation to matrix models and show their link to a class ofnon-commutative field theories invariant under a quantum deformed 3d Poincaresymmetry. This provides a simple relation between matrix models andnon-commutative geometry. Moreover, we review the derivation of effective 2dgroup field theories with non-trivial propagators from Boulatov's group fieldtheory for 3d quantum gravity. Besides the fact that this gives a simple anddirect derivation of non-commutative field theories for the matter dynamicscoupled to (3d) quantum gravity, these effective field theories can beexpressed as multi-matrix models with non-trivial coupling between matrices ofdifferent sizes. It should be interesting to analyze this new class oftheories, both from the point of view of matrix models as integrable systemsand for the study of non-commutative field theories.

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