[Paper Review] AXIAL ANOMALY IN 3HE-A: SIMULATION OF BARYOGENESIS AND GENERATION OF PRIMORDIAL MAGNETIC FIELDS IN MANCHESTER AND HELSINKI

G. E. Volovik|arXiv (Cornell University)|Dec 1, 1998

Quantum, superfluid, helium dynamics59 references16 citations

TL;DR

This paper proposes that superfluid 3He-A provides a condensed-matter analog to high-energy physics phenomena, demonstrating axial anomaly effects via gapless fermionic excitations that mediate non-conservation of charge and momentum. The mechanism enables matter creation without antimatter and generates primordial magnetic fields, with vortex dynamics and counterflow instability mirroring baryogenesis and hypermagnetic field generation in the early universe.

ABSTRACT

Abstract The gapless fermionic excitations in superfluid 3He-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 3He-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 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 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 3He-A.

Motivation & Objective

• To establish 3He-A as a laboratory analog for studying axial anomaly effects in high-energy physics.
• To investigate how chiral fermions in 3He-A lead to non-conservation of charge and momentum, analogous to baryon number violation.
• To explore the connection between vortex dynamics and the conversion of condensate momentum into quasiparticle excitations.
• To model counterflow instability as an analogue to hypermagnetic field generation via the axial anomaly.
• To identify analogs of axions and the hyperphoton mass in the 3He-A system.

Proposed method

• Analyzing the low-energy effective theory of 3He-A, focusing on gapless fermionic modes near gap nodes with relativistic dispersion.
• Deriving effective gravity and gauge fields induced by the chiral fermions in the superfluid state.
• Applying the axial anomaly formalism to describe charge conversion from the condensate (vacuum) to quasiparticles (matter).
• Modeling vortex core dynamics as a spectral flow mechanism transferring momentum from the condensate to the normal component.
• Studying counterflow instability as a process where incoherent flow transforms into coherent order parameter texture.
• Identifying emergent gauge fields and potential axion-like modes in the 3He-A Hamiltonian.

Experimental results

Research questions

• RQ1 How does the axial anomaly in 3He-A lead to non-conservation of quasiparticle charge?
• RQ2 What is the role of vortices in mediating momentum transfer from the condensate to quasiparticles via spectral flow?
• RQ3 How does counterflow instability in 3He-A simulate hypermagnetic field generation in the early universe?
• RQ4 What are the analogs of axions and the hyperphoton in the 3He-A system?
• RQ5 In what way do effective gravity and gauge fields emerge from the chiral fermionic excitations in 3He-A?

Key findings

• The axial anomaly in 3He-A leads to non-conservation of quasiparticle charge, enabling matter creation without antimatter production.
• Vortex core dynamics mediate the conversion of condensate momentum into heat bath excitations, analogous to baryon number violation in cosmic strings.
• Counterflow instability in 3He-A results in the generation of effective gauge fields, mimicking hypermagnetic field production via the axial anomaly.
• The system exhibits emergent gauge fields and potential axion-like modes, with possible mechanisms for hyperphoton mass generation.
• The effective field theory of 3He-A reproduces key features of high-energy physics, including chiral anomaly and spectral flow in topological defects.
• The low-energy dynamics of 3He-A provide a controllable analog for studying baryogenesis and primordial magnetic fields in cosmology.