Nonlocal quantum gravity and M-theory

We construct a ultraviolet completion of the bosonic sector of 11-dimensional supergravity motivated by string field theory. We start from a general class of theories characterized by an entire nonpolynomial form factor that allows one to avoid new poles in the propagator and improves the high-energy behavior of the loops amplitudes. Comparing these models with effective string field theory, a unique form factor is selected out. In view of this, we modify ten-dimensional supergravity and finally get a ultraviolet completion of 11-dimensional supergravity by an oxidation process. The result is a candidate for a finite and unitary particle-field limit of M-theory.

Figure 1

Diagrammatic representation of the completion of 11-dimensional supergravity. At the core of the graph is string field theory, whose limit ${\alpha }^{\prime }\to 0$ is Type-IIA ten-dimensional supergravity. The projection of SFT on the massless sector is nonpolynomial or semipolynomial Type-IIA supergravity. We know that the dimensional reduction of 11-dimensional supergravity to ten dimensions is Type-IIA supergravity plus extra massive states; applying the reverse process, we can oxidate nonpolynomial Type-IIA supergravity to get a nonpolynomial completion of 11-dimensional supergravity (M-theory). Taking the ${\alpha }^{\prime }\to 0$ limit in the M-theory action, we find again the unique 11-dimensional supergravity. In parallel, the ${\alpha }^{\prime }\to 0$ limit of nonpolynomial Type-IIA supergravity is the usual Type-IIA supergravity.