Mixed Anomalies: Chiral Vortical Effect and the Sommerfeld Expansion

Abstract

We discuss the connection between the integer moments of the Fermi distribution function that occur in the Sommerfeld expansion and the coefficients that occur in anomalous conservation laws for chiral fermions. As an illustration we extract the chiral magneto-thermal energy current from the mixed gauge-gravity anomaly in the 3+1 dimensional energy-momentum conservation law. We then use a similar method to confirm the conjecture that the $T^2/12$ thermal contribution to the chiral vortical effect (CVE) current arises from the gravitational Pontryagin term in the 3+1-dimensional chiral anomaly

arXiv comment25 pages, 1 figure, Latex. New version has added references

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• On axial current in rotating and accelerating medium
• Zilch Vortical Effect, Berry Phase, and Kinetic Theory
• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• Nieh-Yan Anomaly: Torsional Landau Levels, central charge and anomalous thermal Hall effect
• Effects of rotation and acceleration in the axial current: density operator vs Wigner function
• Hawking fragmentation and Hawking attenuation in Weyl semimetals
• The Zilch Vortical Effect
• On thermal Nieh-Yan anomaly in Weyl superfluids
• Unruh effect universality: emergent conical geometry from density operator
• Thermodynamics of accelerated fermion gas and instability at Unruh temperature
• CVE for photons: black-hole vs. flat-space derivation
• Hamiltonian approach to the torsional anomalies and its dimensional ladder
• Chiral anomalies induced transport in Weyl semimetals in quantizing magnetic field
• Causal and stable first-order chiral hydrodynamics
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• Thermodynamics and decay of de Sitter vacuum
• Chiral anomalies in 3D spin-orbit coupled metals: electrical, thermal, and gravitational anomaly
• On chiral responses to geometric torsion
• Anomalous gravitomagnetic moment and non-universality of the axial vortical effect at finite temperature
• Hydrodynamic manifestations of gravitational chiral anomaly
• Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals
• Chiral vortical effect for vector fields
• Calculation of acceleration effects using the Zubarev density operator
• Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
• Higher spin vortical Zilches from Kubo formulae
• Chiral Vortical Effect in Extended Rarita-Schwinger Field Theory and Chiral Anomaly
• Tilt induced vortical response and mixed anomaly in inhomogeneous Weyl matter
• Torsion and anomalies in the warped limit of Lifschitz theories
• Gravitational chiral anomaly and anomalous transport for fields with spin 3/2
• Gravitational chiral anomaly for spin 3/2 field interacting with spin 1/2 field
• Out of equilibrium Chiral Vortical Effect in Holography
• On the path integral approach to quantum anomalies in interacting models
• Anomalous Luttinger equivalence between temperature and curved spacetime: From black hole's atmosphere to thermal quenches
• Chiral anomalies in black hole spacetimes
• Zilch Vortical Effect for Fermions
• On chiral vortical effect in accelerated matter
• Anomalous transport from geometry
• Vortical effects in chiral band structures
• Chiral transport in curved spacetime via holography
• Chiral Vortical Transport under Minimal-Length Deformations in Rotating Relativistic Matter