Physical and Formal Presentations of Dual Theory of Electromagnetic Currents

We propose a dynamical Lagrangian theory for the hadron with strong and electromagnetic interactions. We give a simple physical interpretation of our Lagrangian in the parton picture and show explicitly its equivalence with the formal string formulation of the hadron for both the free and interacting Lagrangians. The theory is gauge-invariant with a well-defined conserved current. (The low-energy theorem for currents holds.) The elastic and transition form factors are non-Gaussian and analytic with an infinite series of vector-meson poles. In the two-current channel the electromagnetic amplitude has fixed poles with the imaginary part satisfying rigorously the Dashen-Gell-Mann-Fubini sum rule. In the Bjorken limit our $\nu W_2$ scales and is saturated by narrow resonances. A dispersion relation for $T_2$ continues to hold in the scaling limit and the Gottfried sum rule for $\nu W_2\left(\omega \right)$ is exactly satisfied with the fixed-pole contribution. The hadronic amplitude obtained from the off-shell Compton amplitude is equal to a beta function. In the crossed channel our theory generates Regge poles with quantized intercepts which are degenerate with the vector-meson poles in the off-shell photon line which phenomenologically implies the $\rho -f-A_2$ degeneracy. More generally, we project explicitly hadronic vertices out of our electromagnetic vertex through vector-meson poles and find that these vertices are dual and factorizable.