MG13 - Talk detail

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I introduce a perturbatively super-renormalizable and unitary theory of quantum gravity in any dimension D starting from the four dimensional case. The theory presents two entire functions, a.k.a. "form factors", and a finite number of local operators required by the quantum consistency as well as unitarity (absence of ghosts and any other state) of the theory itself. The theory is power-counting renormalizable at one loop and finite from two loops upward. I essentially present three classes of form factors. At semiclassical level I prove that the gravitational potential is regular in r = 0 for all the choices of form factors compatible with renormalizability and unitarity. For two out of three form factors the black hole solutions are regular with the classical singularity replaced by a "de Sitter-like core" in r=0. For one particular example of form factor, I prove that the D-dimensional "Newtonian cosmology" is singularity-free and the Universe spontaneously follows a de Sitter evolution at the "Planck scale" for any matter content. I conclude stating that, in the ultraviolet regime, the spectral dimension takes on different values for the three cases: less than or equal to "1" for the first case, "0" for the second one and "2" for the third one. Once the class of theories compatible with renormalizability and unitarity is defined, the spectral dimension has the same short-distance "critical value" or "accumulation point" for any value of the topological dimension D. Preliminary results indicate that a nonlocal supergravity theory is power-counting super-renormalizable and tree level unitary with the same particle content of the local N=1 supergravity. In contrast to the local (quadratic-)higher derivative supergravity in its nonlocal generalization all the states fill up in N=1 supergravity multiplet. We believe that the extended SO(N) supergravity, for N=4 and/or N=8, can be off-shell divergence-free also at one loop.

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