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

TL;DR

This paper proposes an all-loop conjecture for reggeon amplitude integrands in N=4 SYM, introducing a new gluing operation in momentum twistor space to derive tree-level and loop integrands, and validates it through BFKL kernel derivation.

Contribution

It introduces a novel gluing operation in momentum twistor space for deriving reggeon amplitudes and loop integrands in N=4 SYM, extending BCFW recursion techniques.

Findings

Derived BCFW recursions for reggeon amplitudes

Predicted reggeon loop integrands in a local integral basis

Computed the LO BFKL kernel 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.