Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction

Abstract

We study the first non-planar correction to gluon scattering amplitudes in $\mathcal{N}=4$ SYM theory. The correction takes the form of a double trace partial amplitude and is suppressed by one power of $1/N$ with respect to the leading single trace contribution. We extend the duality between planar scattering amplitudes and null polygonal Wilson loops to the double trace amplitude. The new duality relates the amplitude to the correlation function of two infinite null polygonal Wilson lines that are subject to a quantum periodicity constraint. We test the duality perturbatively at one-loop order and demonstrate it for the dual string in AdS. The duality allows us to extend the notion of the loop integrand beyond the planar limit and to determine it using recursion relations. It also allows one to apply the integrability-based pentagon operator product expansion approach to the first non-planar order.

arXiv comment50 pages, 17 figures. v2 : typos corrected

References in corpus (35)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Gluon scattering amplitudes at strong coupling
• A semi-classical limit of the gauge/string correspondence
• 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
• Local Integrals for Planar Scattering Amplitudes
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Comments on operators with large spin
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Y-system for Scattering Amplitudes
• An Operator Product Expansion for Polygonal null Wilson Loops
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Form factors at strong coupling via a Y-system
• Notes on the scattering amplitude / Wilson loop duality
• Jumpstarting the all-loop S-matrix of planar N=4 super Yang-Mills
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Exciting the GKP string at any coupling
• Strongly γ-deformed N=4 SYM as an integrable CFT
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• On the collinear limit of scattering amplitudes at strong coupling
• Yangian Symmetry for Bi-Scalar Loop Amplitudes
• On a CFT limit of planar ${\gamma }_i$-deformed $\mathcal{N}=4$ SYM theory
• Relations of loop partial amplitudes in gauge theory by Unitarity cut method
• Quark scattering amplitudes at strong coupling

Cited by in corpus (40)

• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Analytic result for a two-loop five-particle amplitude
• Bi-scalar integrable CFT at any dimension
• A Three-Point Form Factor Through Five Loops
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Handling Handles. Part II. Stratification and Data Analysis
• An Operator Product Expansion for Form Factors
• Continuum limit of fishnet graphs and AdS sigma model
• Implications of nonplanar dual conformal symmetry
• Antipodal Self-Duality for a Four-Particle Form Factor
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Amplitudes at Infinity
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Hexagons and Correlators in the Fishnet Theory
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• Dual conformal invariance for form factors
• Building Bases of Loop Integrands
• Form factor recursion relations at loop level
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Colour-Twist Operators I: Spectrum and Wave Functions
• TBA equations for the Schrödinger equation with a regular singularity
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• Exact scattering amplitudes in conformal fishnet theory
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Gravity loop integrands from the ultraviolet
• Three-point functions at strong coupling in the BMN limit
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• A Two-Loop Four-Point Form Factor at Function Level
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Three-Point Functions in ABJM and Bethe Ansatz
• An Operator Product Expansion for Form Factors II. Born level
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• A short review on TBA equation and scattering amplitude/Wilson loop duality