On the ABJM four-point amplitude at three loops and BDS exponentiation

Abstract

We study the three-loop four-point amplitude in ABJM theory. We determine the dual conformal invariant integrals with highest number of propagators and fix their coefficients by two-particle cuts. Evaluating such a combination of integrals in dimensional regularization we provide evidence for exponentiation of the amplitude, including the finite terms. In addition we show that the three-loop amplitude can be expressed in terms of classical polylogarithms of uniform degree of transcendentality.