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We propose a model for high-T$_{c}$ superconductors, valid for$0\leq\delta\leq\delta_{SC}$, that includes both the spin fluctuations of theCu$^{++}$ magnetic ions and of the O$^{--}$ doped holes. Spin-charge separationis taken into account with the charge of the doped holes being associated toquantum skyrmion excitations (holons) of the Cu$^{++}$ spin background. Theholon effective interaction potential is evaluated as a function of doping,indicating that Cooper pair formation is determined by the competition betweenthe spin fluctuations of the Cu$^{++}$ background and of spins of the O$^{--}$doped holes (spinons). The superconducting transition occurs when the spinonfluctuations dominate, thereby reversing the sign of the interaction. At thispoint ($\delta = \delta_{SC}$), the theory is supersymmetric at short distancesand, as a consequence, the leading order results are not modified by radiativecorrections. The critical doping parameter for the onset of superconductivityat T=0 is obtained and found to be a universal constant determined by the shapeof the Fermi surface. Our theoretical values for $\delta_{SC}$ are in goodagreement with the experiment for both LSCO and YBCO.Comment: RevTex, 4 pages, no figure

physical review. b, condensed matter

Magnetic-texture-driven charge pairing in the spin-fermion Hubbard model and superconductivity in the high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>cuprates

Magnetic-texture-driven charge pairing in the spin-fermion Hubbard model and superconductivity in the high-Tccuprates