Multi-Regge limit of the two-loop five-point amplitudes in N $$ \mathcal{N} $$ = 4 super Yang-Mills and N $$ \mathcal{N} $$ = 8 supergravity

Abstract In previous work, the two-loop five-point amplitudes in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory and N $$ \mathcal{N} $$ = 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 N $$ \mathcal{N} $$ = 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.

Abstract licence: CC BY

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