Heat kernel for Newton-Cartan trace anomalies

TL;DR

This paper calculates the primary trace anomaly for a free non-relativistic scalar field in 2+1 dimensions within a Newton-Cartan geometric framework, revealing a dependence on the scalar's mass and discussing implications for non-relativistic a-theorems.

Contribution

It provides the first explicit computation of the trace anomaly in non-relativistic Newton-Cartan theories and explores its implications for non-relativistic conformal invariance.

Findings

Anomaly proportional to 1/m, with m being the scalar mass

Implications for a non-relativistic a-theorem

Insights into boost invariance in non-relativistic theories

Abstract

We compute the leading part of the trace anomaly for a free non-relativistic scalar in 2+1 dimensions coupled to a background Newton-Cartan metric. The anomaly is proportional to 1/m, where m is the mass of the scalar. We comment on the implications of a conjectured a-theorem for non-relativistic theories with boost invariance.