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of the order parameter which simultaneously shares the properties of many other condensed matter systems such as magnetic materials, liquid crystals, superfluid 4He, Bose-Einstein condensates (BEC) in ultra-cold gases, high-temperature and chiral superconductors, systems exhibiting quantum Hall and spin quantum Hall effects, etc. The other reason is that superfluid 3He belongs to the same universality class and is described by the same topology in momentum space as the Standard Model of weak, strong and electromagnetic interactions. This class is characterized by the existence of topologically stable Fermi points in the excitation spectrum. Close to the Fermi point all the ingredients of the Standard Model and gravity emerge: left-handed and right-handed fermions, gauge bosons, metric field, relativistic invariance and other physical laws. This supports the new paradigm that the elementary particles (quarks and leptons), weak, strong and electromagnetic fields, as well as the gravitational field and space-time itself, are entities which naturally emerge in the low energy corner of the medium called quantum vacuum.

The condensed matter experience tells us that there are two complementary schemes for the classification of quantum vacua, both are based on quantum mechanics which is assumed to be a fundamental theory. The traditional classification – the Grand Unification (GUT) scheme – assumes that fermionic and bosonic fields and gravity are also the fundamental phenomena. They obey the fundamental symmetry which becomes spontaneously broken at low energy, and is restored when the Planck energy scale is approached from below. The Fermi point scenario which we are developing provides a complementary anti-GUT scheme in which the ´fundamental´ symmetry and ´fundamental´ fields of GUT gradually emerge together with ´fundamental´ physical laws when the Planck energy scale is approached from above. The emergence of the ´fundamental´ laws of physics is provided by the general property of topology – robustness to details of the microscopic trans-Planckian physics. In this scheme, fermions are primary objects. Approaching the Planck energy scale from above, they are transformed to the Standard Model chiral fermions and give rise to the secondary objects: gauge fields and gravity. Below the Planck scale, the GUT scenario intervenes giving rise to symmetry breaking at low energy. This is accompanied by formation of composite objects, Higgs bosons, and tiny Dirac masses of quark and leptons. In the GUT scheme, general relativity is assumed to be as fundamental as quantum mechanics, while in the second scheme general relativity is a secondary phenomenon. In the anti-GUT scheme, general relativity is the effective theory describing the dynamics of the effective metric experienced by the effective low-energy fields. It is a side product of quantum field theory or of the quantum mechanics in the vacuum with Fermi point.

Developing this scheme in collaboration with Professor Klinkhamer from Karlsruhe we introduced the notion of the Lorentz-invariant self-sustained quantum vacuum which is characterized by the conserved extensive thermodynamic variable q. We found that in such vacuum the value of the cosmological constant in an emergent-gravity scenario is determined by the self-tuning of this variable. For the perfect quantum vacuum, the equilibrium value q0 adjusts itself so that vacuum energy is nullified. In our considerations, a crucial role is played by the Lorentz invariance of the quantum vacuum, for which there is strong experimental support. A small nonzero value of the cosmological constant is proportional to the perturbation which violates the original Lorentz invariance of the perfect (unperturbed) quantum vacuum. Though the vacuum energy density is governed by processes in the deep ultraviolet vacuum, our approach demonstrates that the thermodynamics of the vacuum energy

Annual Report 2007