Trace anomaly for non-relativistic fermions

Understand

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.