Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization

TL;DR

This paper investigates Lifshitz field theories' stress-energy tensor anomalies, developing a split dimensional regularization framework to compute anomaly coefficients and analyze ambiguities in Lifshitz scale anomalies.

Contribution

It introduces a novel split dimensional regularization method for Lifshitz anomalies and applies it to free scalar theories in 2+1 dimensions.

Findings

Calculated Lifshitz scale anomalies in 2+1 dimensions.

Identified the need for curved spacetime without foliation for trivial terms.

Discussed ambiguities in defining Lifshitz scale anomalies.

Abstract

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. We discuss potential ambiguities in Lifshitz scale anomaly definitions.