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We calculate the most divergent contribution to the non-degenerate sector ofthe self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FKSpin Foam model of Quantum Gravity. We find that such a contribution islogarithmically divergent in the cut-off over the SU(2)-representation spinswhen one chooses the face amplitude guaranteeing the face-splitting invarianceof the foam.We also find that the dependence on the boundary data is differentfrom that of the bare propagator. This fact has its origin in thenon-commutativity of the EPRL-FK Y-map with the projector ontoSL(2,C)-invariant states. In the course of the paper, we discuss in detail theapproximations used during the calculations, its geometrical interpretation aswell as the physical consequences of our result.

Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity