Functional and Local Renormalization Groups

TL;DR

This paper explores the connection between functional and local renormalization groups in two dimensions, revealing their equivalence in describing RG flows and providing tools for explicit computations of key quantities.

Contribution

It establishes the equivalence between Weyl consistency conditions in LRG and RG equations in FRG, enabling explicit FRG representations of the Zamolodchikov-Osborn metric.

Findings

Wess-Zumino action described by derivative expansion with RG-related coefficients

Weyl consistency conditions in LRG are equivalent to FRG RG equations for the c-function

Explicit FRG representation of the Zamolodchikov-Osborn metric provided

Abstract

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.