A Cluster Bootstrap for Two-Loop MHV Amplitudes

Abstract

We apply a bootstrap procedure to two-loop MHV amplitudes in planar N=4 super-Yang-Mills theory. We argue that the mathematically most complicated part (the ${\Lambda }^2{B}_2$ coproduct component) of the n-particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure, supersymmetry, and well-defined collinear limits). We present a concise, closed-form expression which manifests these properties for all n.

v2: a few comments added

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Cited by in corpus (42)

• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
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• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• Landau Singularities from the Amplituhedron
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• Antipodal Self-Duality for a Four-Particle Form Factor
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops
• On factorization of multiparticle pentagons
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• All-Helicity Symbol Alphabets from Unwound Amplituhedra
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Yangian Invariants and Cluster Adjacency in N=4 Yang-Mills
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Bootstrapping a Two-Loop Four-Point Form Factor
• The Two-Loop Remainder Function for Eight and Nine Particles
• Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
• Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory
• Nonperturbative enhancement of superloop at strong coupling
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• Towards NMHV amplitudes at strong coupling
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• On the scattering of gluons in the GKP string
• All two-loop MHV remainder functions in multi-Regge kinematics
• The four-loop six-gluon NMHV ratio function
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Non-Planar On-Shell Diagrams
• Polylogarithm identities, cluster algebras and the N=4 supersymmetric theory
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• A Note on One-loop Cluster Adjacency in N = 4 SYM
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Descent equation for superloop and cyclicity of OPE
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Cluster Functions and Scattering Amplitudes for Six and Seven Points