BFKL approach and six-particle maximally helicity violating amplitude inN=4super Yang-Mills theory

Abstract

We consider the planar MHV amplitude in $\mathcal{N}=4$ supersymmetric Yang-Mills theory for $2\ensuremath{\rightarrow}4$ particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops.