Field theory in superfluid 3He: what are the lessons for particle physics, gravity and high-temperature superconductivity
Abstract
There are several classes of homogeneous Fermi-systems, which are characterized by the topology of the fermionic spectrum: (1) Gapless systems with Fermi-surface; (2) Systems with the gap in the spectrum; (3) Gapless systems with topologically stable point nodes (Fermi points); (4) Gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality class (3). The fermionic quasparticles (particles) in this class are chiral. The collective bosonic modes of the system of class (3) are the effective gauge and gravitational fields. This allowed us to model in 3He-A experiments such phenomena as axial anomaly, baryoproduction and magnetogenesis. The 3He-A textures induce the nontrivial effective metrics of the space, in which the free quasiparticles move along geodesics. One can simulate event horizons, Hawking radiation, etc. High-temperature superconductors belong to the class (4). They have gapless fermionic quasiparticles with the "relativistic" spectrum close to the gap nodes, which allows to apply to them the ideas developed in superfluid 3He-A.Keywords
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