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.
Highlights
Regge theory initially arose from the need to interpret data from high-energy experiments, and played a prominent role in the inception of string theory
As we will describe we find that the two-loop five-particle amplitudes in N = 4 super Yang-Mills and N = 8 supergravity are continuous but not real analytic across the real axis Im[z] = 0
In multi-Regge kinematics, the degrees of freedom of the 5-point amplitude are split into three sets: left-moving (p2, p3), central (p4) and right-moving (p5, p1), which leads to the following factorization: A5 = L|e−ηLH a4e−ηRH |R, (6.1)
Summary
Regge theory initially arose from the need to interpret data from high-energy experiments, and played a prominent role in the inception of string theory. The conceptual progress in understanding the Regge limit in quantum field theory [15,16,17] lead to predictions that were successfully compared against explicit three-loop results for the full-colour four-gluon amplitudes in N = 4 super Yang-Mills [18]. The symbol result allowed to study the Regge limit, and an interesting observation was made: in N = 4 super Yang-Mills, the symbol of the five-particle amplitude vanishes at leading power in the multi-Regge limit [31, 33]!
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