Consistency of local renormalization group in d=3

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. (C) 2013 The Author. Published by Elsevier By. All rights reserved.