  The origin of the pseudogap (PG) phase and superconducting behaviors in
high-Tc superconductors is proposed, based on the picture of Euclidean Q-balls
formation, that carry Cooper/local-pair condensates inside their volumes.
Unlike the baryonic Q-balls in supersymmetric standard model, the Euclidean
Q-balls describe spin-/charge densities, that oscillate in Matsubara time, and
are found in the 'nested' repulsive Hubbard model of high-Tc superconductors.
Euclidean Q-balls arise due to global invariance of the effective theory under
the phase rotation of the Fourier amplitudes of spin-/charge fluctuations,
leading to conservation of the 'Noether charge' Q in Matsubara time. Due to
local minimum of their potential energy at finite amplitude of the density
fluctuations, the Q-balls provide greater binding energy of fermions into
local/Cooper pairs than an exchange with infinitesimal lattice/charge/spin
quasiparticles in the usual Frohlich mechanism. We show that below some
temperature T* the Q-balls arise with a finite density of superconducting
condensate inside them. The Q-balls expand their sizes to infinity at
superconducting transition temperature Tc. Fermionic spectral gap inside the
Q-balls arises in the vicinity of the 'nested' regions of the bare Fermi
surface. Solutions are found analytically from the Eliashberg like equations
with the 'nesting' wave vectors connecting different 'hot spots' on the bare
Fermi surface. The experimental dependences of Uemura (1989) of Tc on
superconducting density n_s, as well as of Li et al. (2010) of diamagnetic
moment on magnetic field above Tc in cuprates follow naturally from the
proposed theory. The 'breathing modes' of the Q-balls in Matsubara time, as
well as sharp maximum in specific heat temperature dependence in the vicinity
of the 1-st order phase transition into Q-balls gas phase are also predicted.
