Weyl Anomaly in NonRelativistic CFTs

TL;DR

This paper investigates the Weyl anomaly in non-relativistic conformal field theories on curved spaces, revealing that anomalies only arise from interactions and not geometry, using both direct and light-cone methods.

Contribution

It demonstrates the absence of geometric Weyl anomalies in non-relativistic CFTs and clarifies the conditions under which anomalies occur, employing multiple analytical approaches.

Findings

No geometric anomaly in non-relativistic Weyl symmetry

Anomalies only appear due to interactions

Light-cone approach confirms the results

Abstract

We study Weyl symmetry for non-relativistic conformal filed theories on curved spatial spaces, and calculate it's quantum anomaly. We show that there is no geometric anomaly, and the non-relativistic Weyl anomaly can appear only due to interaction. Also we study the anomaly by using the light-cone approach.