On chiral magnetic effect in Weyl superfluid 3He-A

TL;DR

This paper investigates the chiral magnetic effect in Weyl superfluid 3He-A, demonstrating how both perturbative and non-perturbative contributions to the Chern-Simons term can be derived without regularization, highlighting the influence of underlying quantum vacuum properties.

Contribution

It provides a regularization-independent analysis of the chiral magnetic effect in 3He-A, revealing two distinct forms of the Chern-Simons term linked to different physical phenomena.

Findings

Both perturbative and non-perturbative Chern-Simons terms are derived from the Adler-Bell-Jackiw equation.

Results agree with microscopic calculations in the trans-Planckian region.

The study shows the dependence of RQFT results on the quantum vacuum properties.

Abstract

In the theory of the chiral anomaly in relativistic quantum field theories (RQFT) some results depend on regularization scheme at ultraviolet. In the chiral superfluid 3He-A, which contains two Weyl points and also experiences the effects of chiral anomaly, the "trans-Planckian" physics is known and the results can be obtained without regularization. We discuss this on example of the chiral magnetic effect (CME), which has been observed in 3He-A in 90's. There are two forms of the contribution of the CME to the Chern-Simons term in free energy, perturbative and non-perturbative. The perturbative term comes from the fermions living in the vicinity of the Weyl point, where the fermions are "relativistic" and obey the Weyl equation. The non-perturbative term originates from the deep vacuum, being determined by the separation of the two Weyl points. Both terms are obtained using the Adler-Bell-Jackiw equation for chiral anomaly, and both agree with the results of the microscopic calculations in the "trans-Planckian" region. Existence of the two nonequivalent forms of the Chern-Simons term demonstrates that the results obtained within the RQFT depend on the specific properties of the underlying quantum vacuum and may reflect different physical phenomena in the same vacuum.