# The all-loop conjecture for integrands of reggeon amplitudes in $\mathcal{N}=4$ SYM

Journal of High Energy Physics, Jun 2018

Abstract In this paper we present the all-loop conjecture for integrands of Wilson line form factors, also known as reggeon amplitudes, in $\mathcal{N}=4$ 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 the BCFW recursions both for tree-level reggeon amplitudes and their loop integrands. In addition we provide predictions for the reggeon loop integrands written in the basis of local integrals. As a check of the correctness of the gluing operation at loop level we derive the expression for LO BFKL kernel in $\mathcal{N}=4$ SYM.

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A. E. Bolshov, L. V. Bork, A. I. Onishchenko. The all-loop conjecture for integrands of reggeon amplitudes in $\mathcal{N}=4$ SYM, Journal of High Energy Physics, 2018, 129, DOI: 10.1007/JHEP06(2018)129