### Speaker

Kevin Falls

### Description

The problem of obtaining a gauge independent beta function
for Newton's constant is addressed. By a specific
parameterisation of metric fluctuations a gauge independent
functional integral is constructed for the semiclassical
theory around an arbitrary Einstein space. The effective
action then has the property that only physical
polarisations of the graviton contribute, while all other
modes cancel with the functional measure. We are then able
to compute a gauge independent beta function for Newton's
constant in d-dimensions to one-loop order. Going beyond the
semiclassical theory, by means of the exact renormalisation
group, the beta function for Newton's constant is found
within a simple approximation exploiting the gauge
independent parameterisation. We then assess the scaling at
an asymptotically safe fixed point. Close to two dimensions
the critical exponent for Newton’s constant is found to be
regulator independent. In four dimensions we apply Litim’s
optimisation criteria on the space of regulators. The
critical exponents is then found to agree with the value
found in numerical lattice simulations by Hamber.