# An analytic result for the two-loop seven-point MHV amplitude in N $\mathcal{N}$ = 4 SYM

John Golden (Department of Physics, Brown University, Box 1843, Providence, RI 02912-1843, U.S.A.) ; Marcus Spradlin (Department of Physics, Brown University, Box 1843, Providence, RI 02912-1843, U.S.A.)

29 August 2014

Abstract: We describe a general algorithm which builds on several pieces of data available in the literature to construct explicit analytic formulas for two-loop MHV amplitudes in N $\mathcal{N}$ = 4 super-Yang-Mills theory. The non-classical part of an amplitude is built from A 3 cluster polylogarithm functions; classical polylogarithms with (negative) cluster X $\mathcal{X}$ - coordinate arguments are added to complete the symbol of the amplitude; beyond-the-symbol terms proportional to π 2 are determined by comparison with the differential of the amplitude; and the overall additive constant is fixed by the collinear limit. We present an explicit formula for the seven-point amplitude R 7 (2) as a sample application.

Published in: JHEP 1408 (2014) 154