We consider two connections between condensed matter and particle physics:
topology of the quantum vacuum and properties of the Higgs modes.
The topological classification of quantum vacua deals with the robust
properties of the fermionic spectrum at the lowest energies. Among the
major universality classes there are: the class of systems with a Fermi
surface; the class of vacua with Fermi points (Weyl, Dirac or Majorana
points); the classes of systems with the Dirac lines and with flat bands;
and the fully gapped vacua. The Fermi point class includes the vacuum of
Standard Model (SM) and the Weyl superfluid 3He-A. In both systems (the
Universe and 3He-A) the low-energy fermionic excitations represent
left-handed and right-handed Weyl fermions, which live near the Weyl or
Dirac points, while the bosonic collective excitations represent the gauge
field bosons, gravitons and Higgs amplitude modes. The chiral properties
of SM, such as chiral anomaly, are determined by symmetry protected
topological invariants in momentum space.
In the broken symmetry phase of SM, its vacuum belongs to the same class
as the fully gapped topological superfluid 3He-B. The order parameter,
which describes spontaneous symmetry breaking in 3He-B, is an analogue of
the Higgs field. Oscillations of the amplitude of the Higgs field
correspond to Higgs bosons, while oscillations of the orientation form
Nambu-Goldstone (NG) modes - SM gauge bosons. In 3He-B there are 14 heavy
Higgs amplitude modes and 1 light Higgs mode, which comes from the
low-energy sector due to the hidden symmetry (small spin-orbit
interaction). The heavy Higgs modes obey the Nambu sum rule, which relates
the masses of Higgs bosons and masses of fermions. If this rule is
applicable to SM, one may expect the extra Higgs bosons with masses 245
GeV and 325 GeV. On the other hand the analogy with the little Higgs
scenario in 3He-B suggests that the observed 125 GeV Higgs could be the
pseudo NG mode acquiring its mass due to violation of a hidden symmetry.