  A theory of the underlying metallic state of large-U$_d$ high-Tc cuprates is
presented starting from the covalent Cu-2O 3-band model associated with a
sufficiently small copper occupancy. U$_d=\infty$ is dealt by the slave fermion
approach. Diagrammatic low order NCA theory in terms of the Cu-O hopping is
supplemented with two independent slave particle chemical potentials which
implement the U(1) local gauge invariance "at average", thus avoiding the
mean-field approximations. The resulting hole spectra consist of itinerant and
localized states. The itinerant states close to the Fermi level are coherent.
They exhibit dichotomies, the copper/oxygen in real and the nodal/antinodal in
reciprocal space. The localized states, related to random Cu-O "mixed valence"
fluctuations within the CuO$_2$ unit cells, are incoherent and fall well away
from the Fermi level. Consequently, Luttinger's band sum rule for the
conduction band is broken. Comparison with IPES, ARPES and NQR data on NCCO,
LSCO, Bi2201 and Bi2212 - in order of increasing correlations - leads to
remarkable agreements considering that only three bare band parameters are
involved.
