Axial anomaly in 3He-A: Simulation of baryogenesis and generation of primordial magnetic field in Manchester and Helsinki

The gapless fermionic excitations in superfluid 3He-A have a "relativistic" spectrum close to the gap nodes. They are the counterpart of the 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 3He-A is discussed in detail. It gives rise to the effect of axial anomaly: conversion of the 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 the vortex dynamics, in which the vortex is the mediator of conversion of linear momentum from the condensate to the normal component via the spectral flow in the vortex core. The same effect leads to the instability of the counterflow in 3He-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 analogs 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 analog of axions and different sources of the mass of the "hyperphoton" in 3He-A.