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

TL;DR

This paper investigates the analyticity properties of multi-Regge limits in Bern-Dixon-Smirnov amplitudes within planar ${ m extbf{N}}=4$ super Yang-Mills theory, contrasting it with flat-space string theory and highlighting discrepancies in analyticity and factorization.

Contribution

It extends previous work to analyze analyticity issues in BDS amplitudes, revealing differences from flat-space string theory in multi-Regge factorization and analyticity constraints.

Findings

BDS amplitudes do not satisfy certain flat-space string analyticity constraints.

Multi-Regge factorization requires trajectories with definite signature.

Discrepancies arise when exponential factors are truncated in the infra-red regulator.

Abstract

As a consequence of the AdS/CFT correspondence, planar ${\cal N} =4$ 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 ${\cal N}=4$ 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 $n\geq 6$. 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 $O(\epsilon)$.