On Newton-Cartan local renormalization group and anomalies
  Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor. 
Roberto Auzzi, Stefano Baiguera, Francesco Filippini and Giuseppe   Nardelli
hep-th