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3He and Universe parallelism

G. E. Volovik
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Abstract

We discuss topological properties of the ground state of spatially homogeneous ensemble of fermions. There are several 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 a class of the gapless systems which is characterized by the Fermi-hypersurface, which is the topologically stable singularity in momentum space. This class contains the conventional Landau Fermi-liquid and also the non-Landau Luttinger Fermi-liquid. Another important 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. Since the spectrum becomes relativistic at low energy, the symmetry of the system is enhanced in the low-energy edge. The low-energy dynamics acquires local invariance, Lorentz invariance and general covariance, which become better and better 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 many phenomena in high energy physics, including axial anomaly. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. Possible simulation in 3He-A of event horizon, Hawking radiation, rotating vacuum and conical space are discussed.

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G. E. Volovik. 1999-04-05. 3He and Universe parallelism. https://arxiv.org/abs/cond-mat/9902171

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