The torsional Chern-Simons term in a non-relativistic Schrodinger-invariant action reproduces, in form, the 1+1 Lifshitz Weyl anomaly on the boundary, though its coefficient is not fixed.
Thermal Hall Effect and Geometry with Torsion
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abstract
We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. It amounts to coupling of the non-relativistic system to the Newton-Cartan geometry with torsion. The approach generalizes the classic Luttinger's formulation of thermal transport. In particular, we clarify the geometric meaning of the fields conjugated to energy and energy current. These fields describe the geometric background with non-vanishing temporal torsion. We use the developed formalism to construct the equilibrium partition function of a non-relativistic system coupled to the NC geometry in 2+1 dimensions and to derive various thermodynamic relations
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A (1+1)-dimensional Lifshitz Weyl Anomaly From a Schr$\mathrm{\ddot{o}}$dinger-invariant Non-relativistic Chern-Simons Action
The torsional Chern-Simons term in a non-relativistic Schrodinger-invariant action reproduces, in form, the 1+1 Lifshitz Weyl anomaly on the boundary, though its coefficient is not fixed.