Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators

Abstract

We propose a dual Wilson loop description for the MHV super form factors of half-BPS operators in planar $\mathcal{N}=4$ super-Yang-Mills theory. In this description, the local operators are represented by on-shell states, made out of zero-momentum particles, that are absorbed by a null periodic super Wilson loop. We present evidence for this duality at weak coupling, by performing an explicit calculation of the Wilson loop matrix elements through one loop. At tree level, the interactions localize at the cusps of the loop, revealing a simple connection between the super form factors and the $m=2$ tree amplituhedron. At loop level, we show that the Wilson loop calculation reproduces the known results for the super form factors. Inspired by this duality, we extend the OPE program developed for the form factors of the Lagrangian to the super form factors of the higher-charge operators. We introduce non-perturbative axioms and conjectures for the main building blocks that govern the exchange of the lightest flux-tube excitations. These blocks appear as simple refinements of the form factor transitions introduced in earlier OPE studies. They are expressed at any value of the 't Hooft coupling in terms of the tilted Beisert-Eden-Staudacher kernel. We carry out checks of our conjectures up to two loops at weak coupling for three- and four-point form factors of half-BPS operators of various lengths, finding perfect agreement with perturbative data.

54 pages, 15 figures, minor corrections, journal version

References in corpus (85)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• The Bethe-Ansatz for N=4 Super Yang-Mills
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Recursion Relations for Tree Amplitudes of Gluons
• Gluon scattering amplitudes at strong coupling
• Transcendentality and Crossing
• 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
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Comments on gluon scattering amplitudes via AdS/CFT
• 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
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Comments on operators with large spin
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• An Operator Product Expansion for Polygonal null Wilson Loops
• Bootstrapping an NMHV amplitude through three loops
• Form factors at strong coupling via a Y-system
• Heptagons from the Steinmann Cluster Bootstrap
• 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
• The super-correlator/super-amplitude duality: Part I
• Analytic two-loop form factors in N=4 SYM
• Basics of Generalized Unitarity
• 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
• Unwinding the Amplituhedron in Binary
• Harmony of Super Form Factors
• Bootstrapping the simplest correlator in planar N = 4 SYM at all loops
• OPE for all Helicity Amplitudes
• Scattering Amplitudes and Wilson Loops in Twistor Space
• Cluster adjacency and the four-loop NMHV heptagon
• The super-correlator/super-amplitude duality: Part II
• Separation of variables for the quantum SL(2,R) spin chain
• The last of the simple remainders
• Are scattering amplitudes dual to super Wilson loops?
• MHV Diagrams in Momentum Twistor Space
• A Three-Point Form Factor Through Five Loops
• Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin
• Exact null octagon
• Nonsinglet pentagons and NMHV amplitudes
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Octagon at finite coupling
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Fermionic pentagons and NMHV hexagon
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• On super form factors of half-BPS operators in N=4 super Yang-Mills
• Folding Amplitudes into Form Factors: An Antipodal Duality
• On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders
• Quantum mechanics of null polygonal Wilson loops
• Clustering and the Three-Point Function
• The SU(2|3) dynamic two-loop form factors
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part I: $\mathcal{N}=4$ super Yang-Mills
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• On Form Factors in N=4 SYM Theory and Polytopes
• An Operator Product Expansion for Form Factors
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• Antipodal Self-Duality for a Four-Particle Form Factor
• Bethe Ansaetze for GKP strings
• Luescher formula for GKP string
• Dual conformal invariance for form factors
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• Matrix pentagons
• On Form Factors and Correlation Functions in Twistor Space
• The Wilson Loop -- Large Spin OPE Dictionary
• Colour-Twist Operators I: Spectrum and Wave Functions
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• An Origin Story for Amplitudes
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• Structure Constants in $\mathcal{N}=4$ SYM and Separation of Variables
• Vertex Operators of Super Wilson Loops
• Determinants in self-dual N=4 SYM and twistor space
• Form factors and correlation functions in N = 4 super Yang-Mills theory from twistor space

Cited by in corpus (4)

• A Two-Loop Four-Point Form Factor at Function Level
• Exploring superconformal Yang-Mills theories through matrix Bessel kernels
• Higher-Point Correlators in N=4 SYM: Generating Functions
• On exactly solvable Yang-Baxter models and enhanced symmetries