An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM

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=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-coordinate arguments are added to complete the symbol of the amplitude; beyond-the-symbol terms proportional to ${\pi }^2$ 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.

17 pages, 1 figure; v2: minor changes; v3: added a section with some background material

References in corpus (5)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Analytic Results for MHV Wilson Loops
• Heptagon Amplitude in the Multi-Regge Regime

Cited by in corpus (7)

• Bootstrapping the QCD soft anomalous dimension
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Cross-Order Integral Relations from Maximal Cuts
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution