  The large U_d theory, based on the Emery three band model extended with the
Ox-Oy hopping t_pp, is constructed for the metallic state of high-Tc cuprates,
using the mapping on the slave fermion theory. The time-dependent diagrammatic
theory in terms of the Cu-O hopping t_pd starts from the locally gauge
invariant state with vanishing occupation of the Cu state and builds a finite
n_d in higher orders. This theory is locally gauge invariant asymptotically,
but replaces the d-p anticommutation between the Cu and O sites by the
commutation and is antisymmetrized a posteriori. Rather than t_pd, the small
parameter of the theory is n_d less or equal to 1/2. The leading many body
effect is band narrowing, different from the mean-field one. It is accompanied
by the d10-d9 intracell charge transfer disorder, which breaks the Luttinger
sum rule for the conduction band. The corresponding damping of the single
particle propagation is situated well below the Fermi level. The effective
local repulsions between the hybridized pdp propagators show up beyond the
third order. The a posteriori antisymmetrization removes the triplet repulsion
between the pdp particles but keeps the singlet repulsion which favors
incommensurate SDW correlations at low energy. Such repulsion is the metallic
counterpart of the superexchange J_pd between the dpd propagators. Resonant
valence bonds thus appear as perturbative corrections. The resulting theory is
shown to compare favorably with numerous experiments, emphasizing the physical
importance of the oxygen degrees of freedom.
