Contents -- 1 Introduction: GUT and anti-GUT -- I: QUANTUM BOSE LIQUID -- 2 Gravity -- 2.1 The Einstein theory of gravity -- 2.2 Vacuum energy and cosmological term -- 3 Microscopic physics of quantum liquids -- 3.1 Theory of Everything in quantum liquids -- 3.2 Weakly interacting Bose gas -- 3.3 From Bose gas to Bose liquid -- 4 Effective theory of superfluidity -- 4.1 Superfluid vacuum and quasiparticles -- 4.2 Dynamics of superfluid vacuum -- 4.3 Normal component - 'matter' -- 5 Two-fluid hydrodynamics -- 5.1 Two-fluid hydrodynamics from Einstein equations -- 5.2 Energy-momentum tensor for 'matter' -- 5.3 Local thermal equilibrium -- 5.4 Global thermodynamic equilibrium -- 6 Advantages and drawbacks of effective theory -- 6.1 Non-locality in effective theory -- 6.2 Effective vs microscopic theory -- 6.3 Superfluidity and universality -- II: QUANTUM FERMIONIC LIQUIDS -- 7 Microscopic physics -- 7.1 Introduction -- 7.2 BCS theory -- 7.3 Vacuum energy of weakly interacting Fermi gas -- 7.4 Spin-triplet superfluids -- 8 Universality classes of fermionic vacua -- 8.1 Fermi surface as topological object -- 8.2 Systems with Fermi points -- 9 Effective quantum electrodynamics in [sup(3)]He-A -- 9.1 Fermions -- 9.2 Effective electromagnetic field -- 9.3 Effective SU(N) gauge fields -- 10 Three levels of phenomenology of superfluid [sup(3)]He -- 10.1 Ginzburg-Landau level -- 10.2 London level in [sup(3)]He-A -- 10.3 Low-temperature relativistic regime -- 10.4 Parameters of effective theory in London limit -- 10.5 How to improve quantum liquid -- 11 Momentum space topology of 2+1 systems -- 11.1 Topological invariant for 2+1 systems -- 11.2 2+1 systems with non-trivial p-space topology -- 11.3 Fermi point as diabolical point and Berry phase -- 11.4 Quantum phase transitions -- 12 Momentum space topology protected by symmetry.

12.1 Momentum space topology of planar phase -- 12.2 Quarks and leptons -- 12.3 Momentum space topology of Standard Model -- 12.4 Reentrant violation of special relativity -- III: TOPOLOGICAL DEFECTS -- 13 Topological classification of defects -- 13.1 Defects and homotopy groups -- 13.2 Analogous 'superfluid' phases in high-energy physics -- 14 Vortices in [sup(3)]He-B -- 14.1 Topology of [sup(3)]He-B defects -- 14.2 Symmetry of defects -- 14.3 Broken symmetry in B-phase vortex core -- 15 Symmetry breaking in [sup(3)]He-A and singular vortices -- 15.1 [sup(3)]He-A and analogous phases in high-energy physics -- 15.2 Singular defects in [sup(3)]He-A -- 15.3 Fractional vorticity and fractional flux -- 16 Continuous structures -- 16.1 Hierarchy of energy scales and relative homotopy group -- 16.2 Continuous vortices, skyrmions and merons -- 16.3 Vortex sheet -- 17 Monopoles and boojums -- 17.1 Monopoles terminating strings -- 17.2 Defects at surfaces -- 17.3 Defects on interface between different vacua -- IV: ANOMALIES OF CHIRAL VACUUM -- 18 Anomalous non-conservation of fermionic charge -- 18.1 Chiral anomaly -- 18.2 Anomalous non-conservation of baryonic charge -- 18.3 Analog of baryogenesis in [sup(3)]He-A -- 18.4 Experimental check of Adler-Bell-Jackiw equation in [sup(3)]He-A -- 19 Anomalous currents -- 19.1 Helicity in parity-violating systems -- 19.2 Chern-Simons energy term -- 19.3 Helical instability and 'magnetogenesis' due to chiral fermions -- 20 Macroscopic parity-violating effects -- 20.1 Mixed axial-gravitational Chern-Simons term -- 20.2 Orbital angular momentum in [sup(3)]He-A -- 20.3 Odd current in [sup(3)]He-A -- 21 Quantization of physical parameters -- 21.1 Spin and statistics of skyrmions in 2+1 systems -- 21.2 Quantized response -- V: FERMIONS ON TOPOLOGICAL OBJECTS AND BRANE WORLD.

22 Edge states and fermion zero modes on soliton -- 22.1 Index theorem for fermion zero modes on soliton -- 22.2 3+1 world of fermion zero modes -- 23 Fermion zero modes on vortices -- 23.1 Anomalous branch of chiral fermions -- 23.2 Fermion zero modes in quasiclassical description -- 23.3 Interplay of p- and r-topologies in vortex core -- 24 Vortex mass -- 24.1 Inertia of object moving in superfluid vacuum -- 24.2 Fermion zero modes and vortex mass -- 24.3 Associated hydrodynamic mass of a vortex -- 25 Spectral flow in the vortex core -- 25.1 Analog of Callan-Harvey mechanism of cancellation of anomalies -- 25.2 Restricted spectral flow in the vortex core -- VI: NUCLEATION OF QUASIPARTICLES AND TOPOLOGICAL DEFECTS -- 26 Landau critical velocity -- 26.1 Landau critical velocity for quasiparticles -- 26.2 Analog of pair production in strong fields -- 26.3 Vortex formation -- 26.4 Nucleation by macroscopic quantum tunneling -- 27 Vortex formation by Kelvin-Helmholtz instability -- 27.1 Kelvin-Helmholtz instability in classical and quantum liquids -- 27.2 Interface instability in two-fluid hydrodynamics -- 28 Vortex formation in ionizing radiation -- 28.1 Vortices and phase transitions -- 28.2 Vortex formation at normal-superfluid interface -- VII: VACUUM ENERGY AND VACUUM IN NON-TRIVIAL GRAVITATIONAL BACKGROUND -- 29 Casimir effect and vacuum energy -- 29.1 Analog of standard Casimir effect in condensed matter -- 29.2 Interface between two different vacua -- 29.3 Force on moving interface -- 29.4 Vacuum energy and cosmological constant -- 29.5 Mesoscopic Casimir force -- 30 Topological defects as source of non-trivial metric -- 30.1 Surface of infinite red shift -- 30.2 Conical space and antigravitating string -- 31 Vacuum under rotation and spinning strings -- 31.1 Sagnac effect using superfluids.

31.2 Vortex, spinning string and Lense-Thirring effect -- 31.3 Gravitational Aharonov-Bohm effect and Iordanskii force on a vortex -- 31.4 Quantum friction in rotating vacuum -- 32 Analogs of event horizon -- 32.1 Event horizons in vierbein wall and Hawking radiation -- 32.2 Painlevé-Gullstrand metric in superfluids -- 32.3 Horizon and singularity on AB-brane -- 32.4 From 'acoustic' black hole to 'real' black hole -- 33 Conclusion -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.