Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory

Abstract

We study the S-matrix of planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics; in particular, the higher-point amplitudes we consider can be obtained from those with lowest-points by a collinear uplifting. Based on a compact formula for one-loop N${}^2$MHV amplitudes, we use an equation proposed previously to compute, for the first time, the complete two-loop NMHV and three-loop MHV octagons, which we conjecture to uplift to give the full $n$-point amplitudes up to simpler logarithmic terms or dilogarithmic terms.

v2: important typos fixed. 38 pages, 4 figures. An ancillary file with two-loop NMHV "remainders" for n=10,12 can be found at http://www.nbi.dk/~schuot/nmhvremainders.zip

References in corpus (19)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• An Operator Product Expansion for Polygonal null Wilson Loops
• Notes on the scattering amplitude / Wilson loop duality
• Finite Temperature Spectral Densities of Momentum and R-Charge Correlators in $\mathbb{N}=4$ Yang Mills Theory
• Leading singularities and off-shell conformal integrals
• Analytic Results for MHV Wilson Loops
• Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica
• Minimal surfaces in AdS and the eight-gluon scattering amplitude at strong coupling
• Some analytic results for two-loop scattering amplitudes
• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion

Cited by in corpus (17)

• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Iterative structure of finite loop integrals
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• Grassmannians for scattering amplitudes in 4d $\mathcal{N}=4$ SYM and 3d ABJM
• Notes on cluster algebras and some all-loop Feynman integrals
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Truncated cluster algebras and Feynman integrals with algebraic letters
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• Cluster Polylogarithms for Scattering Amplitudes
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
• Smooth Wilson Loops in N=4 Non-Chiral Superspace
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras
• Cluster algebras in scattering amplitudes with special 2D kinematics