Space-time S-matrix and Flux-tube S-matrix at Finite Coupling

Abstract

We propose a non-perturbative formulation of planar scattering amplitudes in N=4 SYM or, equivalently, polygonal Wilson loops. The construction is based on the OPE approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named Pentagon transitions. These transitions satisfy a simple relation to the worldsheet S-matrix on top of the so called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this letter we present a subsector of the full solution to scattering amplitudes which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature. For example, the strong coupling Y-system can be understood in this approach.

6 pages, 6 figures

References in corpus (9)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Comments on operators with large spin
• An Operator Product Expansion for Polygonal null Wilson Loops
• Notes on the scattering amplitude / Wilson loop duality

Cited by in corpus (202)

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• The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory
• Hexagonalization of Correlation Functions
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• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
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• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
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• OPE for all Helicity Amplitudes
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• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
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• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
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• QCD Pomeron from AdS/CFT Quantum Spectral Curve
• How tropical are seven- and eight-particle amplitudes?
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• Hexagonalization of Correlation Functions II: Two-Particle Contributions
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• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
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• Tailoring Non-Compact Spin Chains
• Lifting Heptagon Symbols to Functions
• Quantum mechanics of null polygonal Wilson loops
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• Clustering and the Three-Point Function
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• Fixing the Quantum Three-Point Function
• An Operator Product Expansion for Form Factors
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• Continuum limit of fishnet graphs and AdS sigma model
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Dual Conformal Structure Beyond the Planar Limit
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• Towards single-valued polylogarithms in two variables for the seven-point remainder function in multi-Regge-kinematics
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• The Two-Loop Remainder Function for Eight and Nine Particles
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• Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model
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• Lectures on Three-point Functions in N=4 Supersymmetric Yang-Mills Theory
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• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
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• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• An Origin Story for Amplitudes
• Instanton effects in correlation functions on the light-cone
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• Resummed tree heptagon
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• MHV amplitudes at strong coupling and linearized TBA equations
• All orders results for self-crossing Wilson loops mimicking double parton scattering
• Systematics of the Multi-Regge Three-Loop Symbol
• Spinning Hexagons
• Gluing Hexagons at Three Loops
• A Two-Loop Four-Point Form Factor at Function Level
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Antipodal Symmetry of Two-Loop MHV Amplitudes
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• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
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