Structure of the cylinder term in the topological expansion

We discuss the properties of the cylinder beyond the conventional multiperipheral framework, focusing our attention on the possibility of a two-singularity scheme. A sort of hybrid model is proposed where both the usual multiperipheral kernel and the Pomeron singularity are coupled to the Reggeon dipole. We give reasons for expecting in this case a weak $f$ and $\omega$ renormalization, even in SU(2). Using dual field theory as a guide, we discuss several problems related to the cylinder topology: overlap between clusters, daughter exchanges, signature and charge conjugation, and $t_{min}$ cutoffs. Taking the two-particle $s$-channel discontinuity of the one-loop double-twisted graph, we show that the production of two overlapping clusters admits a sort of multiperipheral description where the overlap region is governed by the Pomeron singularity.