On Nieh-Yan transport

Abstract

We study nondissipative transport induced by the Nieh-Yan anomaly. After computing the torsional terms in the equilibrium partition function using transgression, we find the constitutive relations for the covariant axial-vector, heat, stress, and spin currents. A number of new transport effects are found, driven by background torsion and the spin chemical potential. Torsional constitutive relations in two-dimensional systems are also analyzed.

Emergent geometry, torsion and anomalies in non-relativistic topological matter

“…[78,64,90,48,63,89,62]. These responses, symmetries, anomalies and their anomaly polynomials in topological matter will be discussed elsewhere, see [84] for discussion for a relativistic model.…”

“…In non-relativistic topological matter, this is determined by the UV completion and UV cutoff parameters Λ are well-defined a priori. Relativistic models with UV torsional terms were discussed also in [84]. Notwithstanding, at finite temperatures and chemical potentials, relativistic and non-relativistic systems feature anomalous currents from torsion [85,86,87,88,50], similar to the chiral vortical effect induced in hydrodynamics by chiral QFT anomaly [23,29,27].…”

Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral p+ip Weyl condensates

“…In particular, recent work on (non)relativistic hydrodynamic transport with torsion [54,[81][82][83] did not take into account the presence of the Nieh-Yan anomaly terms. See, however, the more recent works [70,83,84] focusing on finite, relativistic UV anomaly terms which we did not discuss here. The results we find with the relativistic Kubo formulas are in exact agreement with previous results, including the simple but physically compelling Landau level approach with and without UV cutoffs [71,76].…”

“…See, e.g., Refs. [80,83,84,[91][92][93][94] and [62][63][64][69][70][71] for more discussions on the UV anomaly in relativistic and nonrelativistic systems. For example, the NY anomaly term can be generated in hydrodynamics with matter, as we discuss in the main text, where Λ is supplemented by the available (low-energy) scales T, μ, m, etc., which we focus on in the main text.…”

In Pursuit of BRST Symmetry and Observables in 4D Topological Gauge-Affine Gravity

“…It was shown that the Nieh-Yan form seems to give the observable effect of chiral anomalies a torsional topological origin [6,7,18] and to enter into the interaction between a spinning particle and a gravitational field in curved spacetime with torsion [19]. Recently, the Nieh-Yan form transport effects were studied via the computation of equilibrium partition functions stemming from a torsional anomaly [20]. Further, the chiral Nieh-Yan anomaly was shown to be related to the hydrodynamic anomaly in superfluid systems [21].…”