Consistency of local renormalization group in d=3

TL;DR

This paper investigates the constraints imposed by Weyl anomaly and local renormalization group consistency conditions in three-dimensional quantum field theories, providing a comprehensive classification and testing their implications.

Contribution

It offers a general classification of consistency conditions and ambiguities in 3D quantum field theories within the power-counting renormalization scheme, with applications to various theories.

Findings

Derived non-trivial constraints on beta functions and anomalous dimensions.

Classified the ambiguities in Weyl anomaly in 3D QFTs.

Validated results through checks in conformal, supersymmetric, and holographic theories.

Abstract

We discuss Weyl anomaly and consistency conditions of local renormalization group in d=1+2 dimensional quantum field theories. We give a classification of the consistency conditions and ambiguities in most generality within the power-counting renormalization scheme. They provide many non-trivial constraints on possible forms of beta functions, anomalous dimensions and Weyl anomaly of general d=1+2 dimensional quantum field theories. We perform modest checks of our results in conformal perturbation theories, supersymmetric field theories and holographic computations.