3D Quantum Gravity and Effective Noncommutative Quantum Field Theory

We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a $\kappa$ deformation of the Poincaré group.

Figure 1

Feynman rules for particles propagation in the Ponzano-Regge model.