Abstract
We describe a general algorithm for the computation of the remainder function for n-gluon scattering in multi-Regge kinematics for strongly coupled planar $$ \mathcal{N}=4 $$ super Yang-Mills theory. This regime is accessible through the infrared physics of an auxiliary quantum integrable system describing strings in AdS5×S5. 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].
Highlights
Incomplete for n ≥ 6 external gluons beyond one-loop order [3,4,5]
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 super Yang-Mills theory
We have presented a general algorithm for the calculation of n-gluon scattering amplitudes in strongly coupled N = 4 SYM in various multi-Regge regions
Summary
The aim of this section is to introduce the relevant kinematic invariants and to discuss their behavior in the multi-Regge limit. For our discussion of 2 → n − 2 production amplitudes, we shall need a particular set of such cross ratios. This is discussed in the first subsection. We turn to the multi-Regge limit and describe how our basis of cross ratios behaves as we go to high energies. The multi-Regge limit is described by the neighborhood of a particular point in the space of cross ratios. In order to exhibit interesting multi-Regge behavior, we must take the limit in various regions. These are discussed in the third subsection
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