The local RG equation and chiral anomalies

Abstract

We generalize the local renormalization group (RG) equation to theories with chiral anomalies. We find that a new anomaly is required by the Wess-Zumino consistency conditions. Taking into account the new anomaly, the trace of the energy momentum tensor is expressed in terms of the covariant flavor currents, instead of the consistent ones. This result is used to show that a flavor rotation induced by the RG flow can be eliminated by a choice of scheme even in the presence of chiral anomalies. As part of a general discussion of chiral anomalies in the presence of background sources, we also derive non-renormalization theorems. Finally, we introduce the $\theta$ parameter as a source, and derive constraints on a perturbative running of this parameter.

References in corpus (8)

• On Renormalization Group Flows in Four Dimensions
• The renormalization of the axial anomaly in dimensional regularization
• The $a$-theorem and the Asymptotics of 4D Quantum Field Theory
• Limit Cycles and Conformal Invariance
• Constraints on RG Flow for Four Dimensional Quantum Field Theories
• CP-violating CFT and trace anomaly
• Local Couplings and Sl(2,R) Invariance for Gauge Theories at One Loop
• Vector Beta function

Cited by in corpus (8)

• Constraints on 3- and 4-loop $\beta$-functions in a general four-dimensional Quantum Field Theory
• The a-function for gauge theories
• On Ambiguities and Divergences in Perturbative Renormalization Group Functions
• The a-function in six dimensions
• Nonrelativistic trace and diffeomorphism anomalies in particle number background
• Perturbative running of the topological angles
• The local renormalization of super-Yang-Mills theories
• Superspace formulation of the local RG equation