Fixed Points of Quantum Gravity from Dimensional Regularisation

Abstract

We investigate $\beta$-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is employed which is sensitive to power-law divergences from mass terms or dimensionful couplings. By construction, this setup respects global and gauge symmetries, including diffeomorphisms, and allows for systematic extensions to higher loop orders. We exemplify this approach in the context of four-dimensional quantum gravity. By computing one-loop $\beta$-functions, we find a non-trivial fixed point. It shows two real critical exponents and is compatible with Weinberg's asymptotic safety scenario. Moreover, the underlying structure of divergences suggests that gravity becomes, effectively, two-dimensional in the ultraviolet. We discuss the significance of our results as well as further applications and extensions to higher loop orders.