Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution

TL;DR

This work analyzes the analytic structure of the $2\to5$ amplitude in planar $\mathcal{N}=4$ SYM under multi-Regge kinematics, focusing on the interplay between Regge poles and Regge cuts across Mandelstam regions. By developing generating-function formalisms for both Regge poles and BDS amplitudes and implementing subtraction schemes, the authors obtain renormalized, conformal Regge-pole expressions in regions where Regge cuts are required to cancel unphysical singularities. They explicitly construct the subtraction coefficients and phases for the $2\to5$ case, deriving the conformal-invariant remainder-function contributions and outlining how these feed into the $n=7$ remainder function $R_7$. The results establish a controlled framework linking Regge-pole renormalization with Regge-cut dynamics in MRK, with clear paths toward higher-point amplitudes and a deeper understanding of the conformal structure in $\mathcal{N}=4$ SYM.

Abstract

We investigate the analytic structure of the $2\to5$ scattering amplitude in the planar limit of $\mathcal{N}=4$ SYM in multi-Regge kinematics in all physical regions. We demonstrate the close connection between Regge pole and Regge cut contributions: in a selected class of kinematic regions (Mandelstam regions) the usual factorizing Regge pole formula develops unphysical singularities which have to be absorbed and compensated by Regge cut contributions. This leads, in the corrections to the BDS formula, to conformal invariant 'renormalized' Regge pole expressions in the remainder function. We compute these renormalized Regge poles for the $2\to5$ scattering amplitude.

Figures (29)

• Figure 1: Notations for the $2 \to n-2$ amplitude
• Figure 2: The signatured $2 \to 2$ amplitude
• Figure 3: The generating function for the $2\rightarrow 3$ production process written in terms of monomials of $\tau_1$, $\tau_2$.
• Figure 4: Two types of propagators in channel $i$.
• Figure 5: Illustration of the term $\tau_1\tau_3$.