Analyticity for multi-Regge limits of the Bern–Dixon–Smirnov amplitudes

As a consequence of the AdS/CFT correspondence, planar N=4 super-Yang–Mills SU(N) theory is expected to exhibit stringy behavior and multi-Regge asymptotic. In this paper we extend our recent investigation to consider issues of analyticity, a central feature of Regge asymptotics. We contrast flat-space open string theory in the planar limit with the N=4 super-Yang–Mills theory, as represented by the Bern, Dixon and Smirnov (2005) 1 (BDS) conjecture for n-gluon scattering, believed to be exact for n=4,5 and modified only by a function of cross-ratios for n⩾6. It is emphasized that multi-Regge factorization should be applied to trajectories with definite signature. A variety of analyticity and factorization constraints realized in flat space string theory are not satisfied by the BDS conjecture, at least when the exponential factors are truncate in the infra-red regulator below O(ϵ).