3He And Universe Parallelism

Abstract

We discuss topological properties of the ground state of a spatially homogeneous ensemble of fermions. There are several universality classes of topologically different fermionic vacua; in each case the momentum space topology of the vacuum determines the low-energy (infrared) properties of the fermionic energy spectrum. Among them there is class of the gapless systems which is characterized by the Fermi-hypersurface. This class contains conventional Landau Fermi-liquid and also Luttinger liquid. Another important universality class of gapless systems is characterized by the topologically stable point nodes (Fermi points). Superfluid 3He-A and electroweak vacuum belong to this universality class. The fermionic quasiparticles (particles) in this class are chiral: close to the Fermi points they are left-handed or right-handed massless relativistic particles. The low-energy dynamics acquires gauge invariance, Lorentz invariance and general covariance, which become better defined when the energy decreases. Interaction of the fermions near the Fermi point leads to collective bosonic modes, which look like effective gauge and gravitational fields. Since the vacuum of superfluid 3He-A and electroweak vacuum are topologically similar, we can use 3He-A for simulation of axial anomaly, event horizons, Hawking radiation, rotating vacuum, conical space, etc.