Four-dimensional deformed special relativity from group field theories

We derive a scalar field theory of the deformed special relativity type, living on noncommutative $\kappa$-Minkowski space-time and with a $\kappa$-deformed Poincaré symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF theory in 4 space-time dimensions. This is done at a nonperturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the noncommutative field theory governs their effective dynamics.