On Newton-Cartan trace anomalies

TL;DR

This paper classifies trace anomalies in 2+1 dimensional non-relativistic Schrödinger theories coupled to Newton-Cartan gravity, revealing similarities to relativistic anomalies and proposing a potential a-theorem in this context.

Contribution

It provides a detailed classification of trace anomalies in non-relativistic theories with Newton-Cartan backgrounds, highlighting their relation to relativistic anomalies and addressing previous overcounting issues.

Findings

Type A anomaly structure is similar to relativistic 3+1D case

Anomaly classification differs from z=2 Lifshitz theories

Erratum corrects overcounting, affecting the presence of Type A anomaly

Abstract

We classify the trace anomaly for parity-invariant non-relativistic Schr\"odinger theories in 2+1 dimensions coupled to background Newton-Cartan gravity. The general anomaly structure looks very different from the one in the z=2 Lifshitz theories. The type A content of the anomaly is remarkably identical to that of the relativistic 3+1 dimensional case, suggesting the conjecture that an a-theorem should exist also in the Newton-Cartan context. Erratum: due to an overcounting of the number of linearly-independent terms in the basis, the type A anomaly disappears if Frobenius condition is imposed. See appended erratum for details. This crucial mistake was pointed out to us in arXiv:1601.06795.