The all-loop conjecture for integrands of reggeon amplitudes in N=4 SYM

Abstract

In this paper we present the all-loop conjecture for integrands of Wilson line form factors, also known as reggeon amplitudes, in N=4 SYM. In particular we present a new gluing operation in momentum twistor space used to obtain reggeon tree-level amplitudes and loop integrands starting from corresponding expressions for on-shell amplitudes. The introduced gluing procedure is used to derive BCFW recursions both for tree-level reggeon amplitudes and their loop integrands. In addition we provide predictions for reggeon loop integrands written in the basis of local integrals. As a check of the correctness of gluing operation at loop level we derive the expression for LO BFKL kernel in N=4 SYM.

arXiv comment47 pages, 14 figures; v3: minor changes, typos corrected

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• Full-color three-loop three-point form factors in N=4 SYM
• Form factor recursion relations at loop level
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• High energy QCD Lipatov's effective action in Euclidean space