Fixed Points of Quantum Gravity from Dimensional Regularisation

TL;DR

This paper uses a non-minimal dimensional regularisation scheme to compute one-loop beta functions in four-dimensional quantum gravity, finding a non-trivial fixed point consistent with asymptotic safety and indicating a two-dimensional effective structure at high energies.

Contribution

It introduces a non-minimal renormalisation scheme for quantum gravity that respects symmetries and extends to higher loops, providing new insights into fixed points and ultraviolet behavior.

Findings

Identifies a non-trivial fixed point in quantum gravity.

Shows compatibility with Weinberg's asymptotic safety.

Suggests gravity becomes two-dimensional in the ultraviolet.

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.