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

Abstract

We investigate the analytic structure of the $2\to 5$ 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 $2\to 5$ scattering amplitude.

46 pages, references added, typos corrected, journal version

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• Cluster adjacency and the four-loop NMHV heptagon
• How tropical are seven- and eight-particle amplitudes?
• Computing one-loop corrections to effective vertices with two scales in the EFT for Multi-Regge processes in QCD
• All-order amplitudes at any multiplicity in the multi-Regge limit
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
• Cluster Polylogarithms for Scattering Amplitudes
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• All two-loop MHV remainder functions in multi-Regge kinematics
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• On a residual freedom of the next-to-leading BFKL eigenvalue in color adjoint representation in planar $\mathcal{N}=4$ SYM
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• The Multi-Regge Limit from the Wilson Loop OPE
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills