The Zilch Vortical Effect

Abstract

We study the question if a helicity transporting current is generated in a rotating photon gas at finite temperature. One problem is that there is no gauge invariant local notion of helicity or helicity current. We circumvent this by studying not only the optical helicity current but also the gauge-invariant "zilch" current. In order to avoid problems of causality, we quantize the system on a cylinder of a finite radius and then discuss the limit of infinite radius. We find that net helicity- and zilch currents are only generated in the case of the finite radius and are due to duality violating boundary conditions. A universal result exists for the current density on the axes of rotation in the high-temperature limit. To lowest order in the angular velocity, it takes a form similar to the well-known temperature dependence of the chiral vortical effect for chiral fermions. We briefly discuss possible relations to gravitational anomalies.

14 pages, 8 figures

References in corpus (9)

• Gravitational Anomaly and Transport
• Interacting fermions in rotation: chiral symmetry restoration, moment of inertia and thermodynamics
• Boundary effects and gapped dispersion in rotating fermionic matter
• Electromagnetic helicity in complex media
• Mixed Anomalies: Chiral Vortical Effect and the Sommerfeld Expansion
• Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions
• Electromagnetic duality anomaly in curved spacetimes
• Edge states and thermodynamics of rotating relativistic fermions under magnetic field
• Optical helicity and Hertz vectors

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