Torsion and anomalies in the warped limit of Lifschitz theories

We describe the physics of fermionic Lifschitz theories once the anisotropicscaling exponent is made arbitrarily small. In this limit the system acquires an enhanced(Carrollian) boost symmetry. We show, both through the explicit computation of the pathintegral Jacobian and through the solution of the Wess-Zumino consistency conditions, thatthe translation symmetry in the anisotropic direction becomes anomalous. This turns outto be a mixed anomaly between boosts and translations. In a Newton-Cartan formulationof the space-time geometry such anomaly is sourced by torsion. We use these results togive an effective field theory description of the anomalous transport coefficients, which wereoriginally computed through Kubo formulas in [1]. Along the way we provide a link withwarped CFTs.