Multidimensional finite quantum gravity

Abstract: We advance a class of unitary higher derivative theories of gravity that realize an ultraviolet completion of Einstein general relativity in any dimension. This range of theories is marked by an entire function, which averts extra degrees of freedom (including poltergeists) and improves the high energy behavior of the loop amplitudes. It is proved that only one-loop divergences survive and the theory can be made super-renormalizable regardless of the spacetime dimension. Moreover, using the Pauli-Villars regularization procedure introduced by Diaz-Troost-van Nieuwenhuizen-van Proeyen (DTPN) and applied to Einstein's gravity by Anselmi, we are able to remove the divergences also at one-loop, making the theory completely finite in any dimension as expected by Anselmi and Asorey-Lopez-Shapiro.