Critical scaling in quantum gravity from the renormalisation group

Abstract

The scaling behaviour of euclidean quantum gravity at an asymptotically safe critical point is studied by means of the exact renormalisation group. Gauge independence is ensured via a specific parameterisation of metric fluctuations introduced in a recent paper. Within a non-perturbative approximation the beta function for Newton's constant takes a simple form to all orders in $\hslash$. A UV fixed point is found to exist for $d\le 7$ spacetime dimensions at which the critical scaling can be assessed. The critical exponent for the Newton's constant $\nu$ is found to be regulator independent close to two dimensions. Applying Litim's optimisation criteria we find $\nu \approx 1/3$ in four spacetime dimensions. This value is in agreement with lattice studies supporting the existence of a second order phase transition between strongly and weakly coupled phases.

1 figure. Version 2: Some remarks added and typos fixed

Cited by in corpus (13)

• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• Renormalization group fixed points of foliated gravity-matter systems
• Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• Scaling Exponents for Lattice Quantum Gravity in Four Dimensions
• The unitary conformal field theory behind 2D Asymptotic Safety
• Splitting Ward identity
• Vacuum Condensate Picture of Quantum Gravity
• Gravitational Fluctuations as an Alternative to Inflation
• Revisit of renormalization of Einstein-Maxwell theory at one-loop
• Quantization of gravity and finite temperature effects
• Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum
• Non-singular Bounce from a Phase transition