Introduction

The problems of perturbative Quantum Field Theory (QFT) in relation to the UV behaviour of gravity have led to widespread pessimism about the possibility of constructing a fundamental QFT of gravity. Instead, we have become accustomed to thinking of General Relativity (GR) as an effective field theory, which only gives an accurate description of gravitational physics at low energies. The formalism of effective field theories provides a coherent framework in which quantum calculations can be performed even if the theory is not renormalizable. For example, quantum corrections to the gravitational potential have been discussed by several authors; see and references therein. This continuum QFT description is widely expected to break down at very short distances and to be replaced by something dramatically different beyond the Planck scale. There is, however, no proof that continuum QFT will fail, and the current situation may just be the result of the lack of suitable technical tools. Weinberg described a generalized, nonperturbative notion of renormalizability called “asymptotic safety” and suggested that GR may satisfy this condition, making it a consistent QFT at all energies. The essential ingredient of this approach is the existence of a Fixed Point (FP) in the Renormalization Group (RG) flow of gravitational couplings. Several calculations were performed using the ∈-expansion around d = 2 dimensions, supporting the view that gravity is asymptotically safe.