Analyticity for Multi-Regge Limits of the Bern-Dixon-Smirnov Amplitudes

Abstract

As a consequence of the AdS/CFT correspondence, planar $\mathcal{N}=4$ 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 $\mathcal{N}=4$ super Yang-Mills theory, as represented by the Bern, Dixon and Smirnov \cite{Bern:2005iz} (BDS) conjecture for n-gluon scattering, believed to be exact for $n=4,5$ and modified only by a function of cross-ratios for $n\ge 6$. 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 $O(\epsilon )$.

Published version of the paper, which includes an expanded discussion on Steinmann Relation for 5-point function, (sect. 4.3 and footnotes #9 and #10) as well as additional clarifying comments on how this work compares to other recent related works in the concluding section. 74 pages, 17 figures

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