Critical scaling in quantum gravity from the renormalisation group

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 $\mathrm{\hslash }$. 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 $\nu \approx 1\mathrm{/}3$ 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.