Analytic properties of high-energy production amplitudes in $N{=}4$ SUSY

We investigate the analytic properties of the six-point planar amplitude in $N=4$ SUSY in the multi-Regge kinematics for final-state particles. For inelastic processes, the Steinmann relations play an important role because they allow fixing the phase structure of contributions from the Regge pole and Mandelstam cut. These contributions are invariant under the Möbius transformation in the transverse momentum subspace. The analyticity and factorization properties allow reproducing the two-loop correction to the six-point Bern–Dixon–Smirnov amplitude in $N=4$ SUSY previously obtained in the leading logarithmic approximation using the $s$-channel unitarity. We also investigate the exponentiation hypothesis for the so-called remainder function in the multi-Regge kinematics. The six-point amplitude in the leading logarithmic approximation can be completely reproduced from the Bern–Dixon–Smirnov ansatz using the analyticity and Regge factorization.