Critical scaling in quantum gravity from the renormalisation group

Original · EN

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 ℏ. A UV fixed point is found to exist for d≤ 7 spacetime dimensions at which the critical scaling can be assessed. The critical exponent for the Newton's constant ν is found to be regulator independent close to two dimensions. Applying Litim's optimisation criteria we find ν≈ 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.