On Ward Identities in Lifshitz-like Field Theories

TL;DR

This paper develops a normal product algorithm for anisotropic Lifshitz-like field theories, enabling the construction of symmetry generators and analysis of potential anomalies, exemplified by the dilatation anomaly in a scalar z=2 model.

Contribution

It introduces a novel normal product algorithm tailored for anisotropic field theories and applies it to study symmetry anomalies.

Findings

Constructed symmetry generators for Lifshitz-like theories

Identified potential dilatation anomalies in a scalar model

Provided a framework for anomaly detection in anisotropic theories

Abstract

In this work, we develop a normal product algorithm suitable to the study of anisotropic field theories in flat space, apply it to construct the symmetries generators and describe how their possible anomalies may be found. In particular, we discuss the dilatation anomaly in a scalar model with critical exponent z=2 in six spatial dimensions.