Axial anomaly in 3He-A:

Abstract

The gapless fermionic excitations in superfluid 3 He-A have a "relativistic" spectrum close to the gap nodes. They are the counterpart of chiral particles (left-handed and right-handed) in high energy physics above the electroweak transition. We discuss the effective gravity and effective gauge fields induced by these massless fermions in the low-energy corner. The interaction of the chiral fermions with the gauge field in 3 He-A is discussed in detail. It gives rise to the effect of axial anomaly: Conversion of charge from the coherent motion of the condensate (vacuum) to the quasiparticles (matter). The charge of the quasiparticles is thus not conserved. In other words, matter can be created without creating antimatter. This effect is instrumental for vortex dynamics, in which the vortex is the mediator of conversion of linear momentum from the condensate to the normal component via spectral flow in the vortex core. The same effect leads to the instability of the counterflow in 3 He-A, in which the flow of the normal component (incoherent degrees of freedom) is transformed to the order parameter texture (coherent degrees of freedom). We discuss the analogues of these phenomena in high energy physics. The conversion of the momentum from the vortex to the heat bath is equivalent to the nonconservation of baryon number in the presence of textures and cosmic strings. The counterflow instability is equivalent to the generation of the hypermagnetic field via the axial anomaly. We discuss also an analogue of axions and different sources of the mass of the "hyperphoton" in 3 He-A.

Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory

“…If an electric field is applied parallel to the magnetic field, one will observe the disappearance of left-chiral particles and the appearance of right-chiral anti-particles (or vice versa, depending on the sign of the electric field), so that the total electric charge is conserved. This is the manifestation of the axial anomaly; see the discussion in, e.g., Volovik (1998). Now, let us introduce finite temperature and chemical potentials µ L , µ R and fill both left-and right-chiral branches of the lowest Landau level according to the Fermi-Dirac distribution (see Fig.…”

Black hole and hawking radiation by type-II Weyl fermions

“…The Weyl point with higher Chern numbers, |N 3 | > 1, describes the higher order touching of two energy bands. 6 Weyl fermions exist in chiral superfluid 3 He-A, where the corresponding effects -the chiral anomaly 5,7 and chiral magnetic effect 8,9 -have been experimentally observed. They Weyl fermions are also typical in topological semimetals.…”

The Theory of Everything

“…The Higgs mechanism is nothing but superconductivity with a few technical modifications (31). Dirac fermions, spontaneous breaking of CP, and topological defects all occur in the low-energy spectrum of superfluid 3 He (32)(33)(34).…”