Nonrelativistic trace and diffeomorphism anomalies in particle number background

TL;DR

This paper computes nonrelativistic trace anomalies in Schrödinger theories with background gauge fields, revealing unique nonrelativistic features and gauge non-invariance, using the heat kernel method.

Contribution

It provides the first explicit calculation of nonrelativistic trace anomalies in flat spacetime with background gauge fields for particle number symmetry.

Findings

Anomalies are non-gauge-invariant, unlike relativistic cases.

Gravitational anomaly for a nonrelativistic scalar vanishes.

Results are specific to nonrelativistic Schrödinger theories.

Abstract

Using the heat kernel method, we compute nonrelativistic trace anomalies for Schr\"odinger theories in flat spacetime, with a generic background gauge field for the particle number symmetry, both for a free scalar and a free fermion. The result is genuinely nonrelativistic, and it has no counterpart in the relativistic case. Contrary to the naive expectations, the anomaly is not gauge-invariant; this is similar to the non-gauge covariance of the non-abelian relativistic anomaly. We also show that, in the same background, the gravitational anomaly for a nonrelativistic scalar vanishes.