Functional and Local Renormalization Groups

Understand

We discuss the relation between functional renormalization group (FRG) and local renormalization group (LRG), focussing on the two dimensional case as an example.

• We show that away from criticality the Wess-Zumino action is described by a derivative expansion with coefficients naturally related to RG quantities.
• We then demonstrate that the Weyl consistency conditions derived in the LRG approach are equivalent to the RG equation for the $c$-function available in the FRG scheme.
• This allows us to give an explicit FRG representation of the Zamolodchikov-Osborn metric, which in principle can be used for computations.