Thermal transport, geometry, and anomalies

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

“…We find that the coefficient is nonzero and directly related to that of the CVE (at the level of linear response) and in accordance with the previous results found with, e.g., the simple Landau level approach to chiral torsional anomalies [62,71]. In particular, recent papers [38,80] finding no torsional contribution can be easily incorporated with our framework by noting that when computing the linear response around flat space, torsion has been actually set to zero with only purely metric variations. Nevertheless, we find that nonzero transport coefficients in the case torsionful sources do appear.…”

“…On the other hand, resting on the analogy with gravity, the appearance of the static, equilibrium anomaly transport coefficients can be organized as an order-by-order derivative expansion of the hydrodynamic conservation laws on nontrivial geometric backgrounds with sources [44][45][46][47]. The gravitational (i.e., thermal [38,48]) CVE anomaly current at linear order in response has been related to the gravitational anomalies [15,47,49] that, at least naively, appear only at higher orders in the hydrodynamic gradient expansion. The precise way in which higher-order anomalies can contribute to the transport has led to many useful insights about relativistic and nonrelativistic hydrodynamics, e.g., Refs.…”

“…[80] (see also Ref. [38]) regarding torsion are not correct. In particular, torsion leads to nonvanishing, independent currents with similar anomaly coefficients as for CVE.…”

Quantum Field Theory Anomalies in Condensed Matter Physics

“…10. The physical consequences of gravitational anomalies in higher-dimensional topological states of matter is a topic of active research, and we refer to the more advanced review [84] for recent achievements.…”

“…Not surprisingly, one can also use anomalies to extract the thermal response of 3d TIs by coupling to gravity and using (215). We will not pursue this here, but refer to [84] for a good explanation with references to the original literature.…”