Reggeon phases and the dual bootstrap program

Analyticity requirements lead to complex Regge vertices in multiparticle production amplitudes. Their effect is discussed within a dual, unitary and exchange-degenerate multi-Regge model. A resulting complex Regge vertex is incorporated in fixed-t model calculations of the reggeon bootstrap and the topological pomeron. The bootstrap condition for particle-particle scattering is unaffected but new j-plane singularities appear in Regge-Regge scattering amplitudes. The pomeron and reggeon intercepts determine the two parameters of our Regge vertex and admit two possible solutions: one is close to the naive phase rule (real vertex) and the other is complex and leads to a high lying non-leading pole in the pomeron channel.