Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loops

We show that the four-loop four-point amplitudes of N = 5 supergravity are ultraviolet finite in four dimensions, contrary to expectations based on supersymmetry and duality-symmetry arguments. We explain why the diagrams of any covariant local formalism cannot manifestly exhibit the necessary cancellations for finiteness but instead require a new type of ultraviolet cancellation that we call an “enhanced cancellation”. We also show that the three-loop four-point amplitudes in N = 4 and N = 5 supergravity theories display enhanced cancellations. To construct the loop integrand, we use the duality between color and kinematics. We apply standard methods for extracting ultraviolet divergences in conjunction with the FIRE5 integral reduction program to arrive at the four-loop results. PACS numbers: 04.65.+e, 11.15.Bt, 11.25.Db, 12.60.Jv