Analytic properties of high energy production amplitudes in N=4 SUSY

TL;DR

Analyzes the analytic structure of the six-point planar amplitude in $N=4$ SUSY within the multi-Regge kinematics, focusing on Steinmann constraints and the interplay between Regge-pole and Mandelstam-cut contributions. The work derives a dispersion representation and shows that analyticity and Regge factorization reproduce the two-loop correction to $M_{2->4}$ and probe the exponentiation of the remainder function, highlighting that a pure phase for the remainder (c = e^{iφ}) is incompatible at higher orders. It emphasizes that Mandelstam cuts and Regge-factorized pole terms must be combined in MRK, consistent with BFKL/BKP integrability in the planar limit. Overall, the results suggest that the MRK six-point amplitude can be reconstructed from the BDS ansatz when the correct cut structure and phase relations are enforced.

Abstract

We investigate analytic properties of the six point planar amplitude in N=4 SUSY at the multi-Regge kinematics for final state particles. For inelastic processes the Steinmann relations play an important role because they give a possibility to fix the phase structure of the Regge pole and Mandelstam cut contributions. These contributions have the Moebius invariant form in the transverse momentum subspace. The analyticity and factorization constraints allow us to reproduce the two-loop correction to the 6-point BDS amplitude in N=4 SUSY obtained earlier in the leading logarithmic approximation with the use of the s-channel unitarity. The exponentiation hypothesis for the remainder function in the multi-Regge kinematics is also investigated. The 6-point amplitude in LLA can be completely reproduced from the BDS ansatz with the use of the analyticity and Regge factorization.