Consistency of local renormalization group in d=3

Understand

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.