A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills

Abstract

We study a scalar component of the 8-point next-to-next-to-maximally-helicity-violating (N${}^2$MHV) amplitude at two-loop level in $\mathcal{N}=4$ super-Yang-Mills theory; it has a leading singularity proportional to the inverse of the four-mass-box square root and receives contributions from only two types of non-trivial integrals with one-loop infrared (IR) divergences. We compute such two-loop 8-point integrals by taking (double-)collinear limits of certain finite, dual-conformal-invariant integrals, and they nicely give the IR-safe ratio function after subtracting divergences. As the first genuine two-loop N${}^2$MHV amplitude computed explicitly, we find remarkable structures in its symbol and alphabet: similar to the next-to-MHV (NMHV) case, there are still 9 algebraic letters associated with the square root, and the latter also becomes a letter for the first time; unlike the NMHV case, such algebraic letters appear at either one or all of the second, third and last entry, and the part with three odd letters is particularly simple.

arXiv comment20 pages, 2 figures and an ancillary file containing symbols of two-loop integrals and the ratio function

References in corpus (64)

• Review of AdS/CFT Integrability: An Overview
• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Amplituhedron
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• On planar gluon amplitudes/Wilson loops duality
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• A Duality For The S Matrix
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• From polygons and symbols to polylogarithmic functions
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• PolyLogTools - Polylogs for the masses
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Null polygonal Wilson loops and minimal surfaces in Anti-de-Sitter space
• Scattering into the fifth dimension of N=4 super Yang-Mills
• An Operator Product Expansion for Polygonal null Wilson Loops
• Bootstrapping an NMHV amplitude through three loops
• Uniqueness of two-loop master contours
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Notes on the scattering amplitude / Wilson loop duality
• Heptagons from the Steinmann Cluster Bootstrap
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Pulling the straps of polygons
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Two-Loop Polygon Wilson Loops in N=4 SYM
• Cluster adjacency and the four-loop NMHV heptagon
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• How tropical are seven- and eight-particle amplitudes?
• Lifting Heptagon Symbols to Functions
• Tropical Grassmannians, cluster algebras and scattering amplitudes
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• The elliptic double box and symbology beyond polylogarithms
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Notes on cluster algebras and some all-loop Feynman integrals
• Tropical fans, scattering equations and amplitudes
• Symbol Alphabets from Plabic Graphs
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• Truncated cluster algebras and Feynman integrals with algebraic letters
• Schubert Problems, Positivity and Symbol Letters
• A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Feynman Integrals and Scattering Amplitudes from Wilson Loops
• A Note on Letters of Yangian Invariants
• The Wilson-loop $d\log$ representation for Feynman integrals
• The Three-loop MHV Octagon from $\bar{Q}$ equations
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder

Cited by in corpus (3)

• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Cutting the traintracks: Cauchy, Schubert and Calabi-Yau