  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.
