Topological supersymmetric structure of hadron cross sections

A way of fully implementing unitarity and confinement in the framework of a dual-topological-unitarization theory, including not only mesons but also baryons, has recently been found. This theory consists in the topological description of hadron interactions in terms of two two-dimensional surfaces (a closed "quantum" surface and a bounded "classical" surface). We show that this description directly leads, at the zeroth order of the topological expansion, to certain relations between hadron cross sections, in nice agreement with experimental data. A new topological suppression mechanism is shown to play an important dynamical role. We also point out a new topological supersymmetry property, which leads to realistic experimental consequences. A possible topological origin of the $\rho$ and $\omega$ universality relations emerges as a by-product of our study.