Functional and Local Renormalization Groups

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.

19 pages, 1 figure

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Cited by in corpus (9)

• The nonperturbative functional renormalization group and its applications
• Vacuum effective actions and mass-dependent renormalization in curved space
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• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows
• Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\to \infty$ limit in $O(N)$-type models
• Conformal anomaly from gauge fields without gauge fixing
• Abelian Chern-Simons vortices in the presence of magnetic impurities
• Weyl Consistency Conditions from a local Wilsonian Cutoff
• Gradient Flow and Holography from a Local Wilsonian Cutoff