Constraints on reggeon amplitudes from analyticity and planar unitarity

Using planar dual amplitudes as a guide, we discuss some features of reggeon amplitudes which are relevant in the context of the topological expansion. We look into the analytic properties and, in particular, discuss the validity of finite-mass sum rules for reggeon-reggeon scattering. We investigate the form taken by planar unitarity when a multiperipheral assumption is added. The integral equations obtained are not of the standard Chew-Goldberger-Low type. We find that pure pole-type solutions (i.e. without Regge cuts) to planar unitarity are possible in a way consistent with the symmetry and factorization properties of reggeon-reggeon amplitudes. The appearance of "good" FMSR in the unitarity integrals follows from a careful treatment of phase space - all possible configurations are counted uniquely - and is crucial in achieving the cut cancellation. Throughout the paper we emphasize various subtle points that have been overlooked in the literature.