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Divergences in Spinfoam Quantum Gravity

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The most relevant evidences in favour of the Lorentzian EPRL-FK spinfoam model come from its capibility of reproducing the expected semiclassical limit in the large spin regime. The main examples of this are the large spin limit of the vertex amplitude, later extended to arbitrary triangulations, and that of the spinfoam graviton propagator, which was calculated on the simplest possible two complex. These results are very promising. Nonetheless, their relevance may be endangered by the effects associated to radiative corrections. In this seminar, I will focus on the role played by the simplest diverging graph, the so called 'melon graph', which is known to play a fundamental role in tensorial group field theories. In particular, I will discuss its most divergent part and its geometrical interpretation. I will finally comment on the result, with particular attention to its physical consequences, especially in relation with the semiclassical limit of the spinfoam graviton propagator.