4d Deformed Special Relativity from Group Field Theories

We derive a scalar field theory of the deformed special relativity type, living on non-commutative kappa-Minkowski spacetime and with a kappa-deformed Poincare 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 non-perturbative 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 non-commutative field theory governs their effective dynamics.