The structure of the dual topological expansion is studied up to the cylinder level by concentrating on the determination of Reggeon and Pomeron slopes. A precise formulation for the generation of Regge behavior in terms of an effective random walk is presented, and a well-defined meaning is provided for the trajectory slope in terms of average step lengths in the rapidity and the impact-parameter directions. The smallness of the Pomeron slope, $\frac{{\alpha }_P^{\prime }}{{\alpha }_0^{\prime }}\sim 0.3$, is shown to represent a nontrivial constraint for theories satisfying the requirement of short-range ordering; a topological phase consideration is shown to be the primary mechanism responsible for this phenomenon. The relation between our finding to the naive expectation $\frac{{\alpha }_P^{\prime }}{{\alpha }_0^{\prime }}\simeq \frac{1}{2}$, based on a string picture and to the general phenomenon of the $\frac{f}{P}$ identity is clarified.

• Received 19 November 1979

DOI:https://doi.org/10.1103/PhysRevD.22.1024