Asymptotic safety of gravity coupled to matter

Nonperturbative treatments of the UV limit of pure gravity suggest that it admits a stable fixed point with a positive Newton constant and a cosmological constant. We prove that this result is stable under the addition of a scalar field with a generic potential and nonminimal coupling to the scalar curvature. There is a fixed point where the mass and all nonminimal scalar interactions vanish, while the gravitational couplings have values which are almost identical to those in the pure gravity case. We discuss the linearized flow around this fixed point and find that the critical surface is four dimensional. In the presence of other, arbitrary, massless minimally coupled matter fields, the existence of the fixed point, the sign of the cosmological constant, and the dimension of the critical surface depend on the type and number of fields. In particular, for some matter content, there exist polynomial asymptotically free scalar potentials, suggesting a gravitational solution to the well-known problem of triviality.