Functional approach to dual quark models

The usual N-point Veneziano amplitude can be obtained by summing over a large class of fishnet diagrams if one assumes a φ{symbol}^′4 interaction and suitable approximations. By adding fermion (quark) propagators along the edges of these fishnet diagrams, we obtain a natural generalization of this functional approach to include mesons and baryons without exotics, which smoothly extrapolates to the multiplicative model. By functionally integrating over a two-dimensional strip, we can introduce creation and annihilation operators and solve for the generators of the conformal group. We have not been able to find the mechanism to kill spin ghosts. And because all functional integrations are difficult to perform, we approximate the amplitude by a perturbation series. Because the series in this approximation diverges, the renormalization scheme is also discussed. SU(3) breaking can be introduced in a natural way.