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

Abstract

Abstract In this paper we present the all-loop conjecture for integrands of Wilson line form factors, also known as reggeon amplitudes, in $$ \mathcal{N}=4 $$ 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 $$ \mathcal{N}=4 $$ N = 4 SYM.