Trace anomaly for non-relativistic fermions

Abstract

We study the coupling of a 2+1 dimensional non-relativistic spin 1/2 fermion to a curved Newton-Cartan geometry, using null reduction from an extra-dimensional relativistic Dirac action in curved spacetime. We analyze Weyl invariance in detail: we show that at the classical level it is preserved in an arbitrary curved background, whereas at the quantum level it is broken by anomalies. We compute the trace anomaly using the Heat Kernel method and we show that the anomaly coefficients a, c are proportional to the relativistic ones for a Dirac fermion in 3+1 dimensions. As for the previously studied scalar case, these coefficents are proportional to 1/m, where m is the non-relativistic mass of the particle.

23 pages

References in corpus (7)

• Lifshitz Space-Times for Schroedinger Holography
• Heat kernel methods for Lifshitz theories
• Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization
• Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory
• On Newton-Cartan local renormalization group and anomalies
• Heat kernel for Newton-Cartan trace anomalies
• Physical stress, mass, and energy for non-relativistic matter

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• BMS Field Theories and Weyl Anomaly
• Nonrelativistic trace and diffeomorphism anomalies in particle number background
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory