Equivalence between pairing and staggered-flux-like vorticity of the current-current correlation function in weakly doped antiferromagnets

We show that patterns of the current-current correlation function in the fo rm of the staggered flux indicate that spin bipolarons form in doped antife rromagnets. Holes which form a spin bipolaron reside at opposite ends of a line (string) formed by the defects in the antiferromagnetic spin backgroun d. The string is relatively highly mobile, because the motion of a hole at its end does not raise extensively the number of defects, provided that the hole at the other end of the line follows along the same track. Appropriat e coherent combinations of string states realize some irreducible represent ations of the point group C-4v. Creep of strings favors d- and p-wave state s. Some more subtle processes decide the symmetry of pairing. The pattern o f the current correlation function, that defines the structure of flux, eme rges from motion of holes at string ends and coherence factors with which s tring states appear in the wave function of the bound state. Condensation o f bipolarons and phase coherence between them puts to infinity the correlat ion length of the current correlation function and establishes the flux in the system.