A bstract We describe a general algorithm for the computation of the remainder function for n -gluon scattering in multi-Regge kinematics for strongly coupled planar N = 4 $$ mathcal{N}=4 $$ super Yang-Mills theory. This regime is accessible through the infrared physics of an auxiliary quantum integrable system describing strings in AdS~(5) × S_(5). Explicit formulas are presented for n = 6 and n = 7 external gluons. Our results are consistent with expectations from perturbative gauge theory. This paper comprises the technical details for the results announced in [1].
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