Introduction to Exact Renormalization Group Equation

Einstein’s theory of gravity is not renormalizable, that is, we need infinitely many counter terms to cancel the divergences coming from the bare action. One approach to resolve this problem is called Asymptotic Safety where a non-renormalizable theory can still make sense if the coupling constants of the theory reach a fixed point in the UV. This talk will be about the Exact Renormalization Group Equation or Wetterich equation that can in principle provide a non-perturbative way to calculate the running of couplings. In practice, however, one needs to make perturbative assumptions to solve this equation for a particular QFT. I will illustrate this point by calculating the Wilson-Fisher fixed point and if time permits give a sketch of how to do these calculations in a gravitational theory.