Nonrelativistic trace and diffeomorphism anomalies in particle number background

Abstract

Using the heat kernel method, we compute nonrelativistic trace anomalies for Schrödinger 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.

arXiv comment20 pages; V2 minor changes also in title, typos

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• Non-relativistic Conformal Field Theory in the Presence of Boundary
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Developments in non-relativistic field theory and complexity