Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\\mathcal{N} = 4$ Super Yang-Mills and $\\mathcal{N} = 8$ Supergravity
Caron-Huot, S., Chicherin, D., Henn, J., Zhang, Y., Zoia, S.
Abstract
In previous work, the two-loop five-point amplitudes in $\\mathcal{N}=4$ super Yang-Mills theory and $\\mathcal{N}=8$ supergravity were computed at symbol level. In this paper, we compute the full functional form. The amplitudes are assembled and simplified using the analytic expressions of the two-loop pentagon integrals in the physical scattering region. We provide the explicit functional expressions, and a numerical reference point in the scattering region. We then calculate the multi-Regge limit of both amplitudes. The result is written in terms of an explicit transcendental function basis. For certain non-planar colour structures of the $\\mathcal{N}=4$ super Yang-Mills amplitude, we perform an independent calculation based on the BFKL effective theory. We find perfect agreement. We comment on the analytic properties of the amplitudes.