The Zilch Vortical Effect

TL;DR

This paper investigates the generation of helicity and zilch currents in a rotating photon gas at finite temperature, revealing boundary-condition-dependent effects and universal high-temperature behavior.

Contribution

It introduces the gauge-invariant zilch current as a tool to study helicity transport in rotating photon gases, highlighting boundary effects and universal high-temperature limits.

Findings

Net helicity and zilch currents occur only with finite radius boundary conditions.

A universal current density formula is derived for high temperatures on the rotation axis.

The current's temperature dependence resembles the chiral vortical effect for fermions.

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.