Gravitational anomalies on the Newton-Cartan background

Understand

We derive the trace and diffeomorphism anomalies of the Schr\"odinger field minimally coupled to the Newton-Cartan background using Fujikawa's path integral approach.

• This approach in particular enables us to calculate the one-loop contributions due to all the fields of the Newton-Cartan structure.
• We determine the coefficients and demonstrate that gravitational anomalies for this theory always arise in odd dimensions.
• Due to the gauge field contribution of the background we find that in $2+1$ dimensions the trace anomaly contains terms which have a form similar to that of the $1+1$ and $3+1$ dimensional relativistic trace anomalies.