Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization

Understand

We analyze the structure of the stress-energy tensor correlation functions in Lifshitz field theories and construct the corresponding anomalous Ward identities.

• We develop a framework for calculating the anomaly coefficients that employs a split dimensional regularization and the pole residues.
• We demonstrate the procedure by calculating the free scalar Lifshitz scale anomalies in $2+1$ spacetime dimensions.
• We find that the analysis of the regularization dependent trivial terms requires a curved spacetime description without a foliation structure.