An Operator Product Expansion for Form Factors

Abstract

We propose an operator product expansion for planar form factors of local operators in $\mathcal{N}=4$ SYM theory. This expansion is based on the dual conformal symmetry of these objects or, equivalently, the conformal symmetry of their dual description in terms of periodic Wilson loops. A form factor is decomposed into a sequence of known pentagon transitions and a new universal object that we call the "form factor transition". This transition is subject to a set of non-trivial bootstrap constraints, which we expect to be sufficient to fully determine it. We evaluate the form factor transition for MHV form factors of the chiral half of the stress tensor supermultiplet at leading order in perturbation theory and use it to produce OPE predictions at any loop order. We match the one-loop and two-loop predictions with data available in the literature.

arXiv comment7 pages, 5 figures. v2: references added, convention changed

References in corpus (45)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• Comments on gluon scattering amplitudes via AdS/CFT
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Bootstrapping the three-loop hexagon
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• Form factors at strong coupling via a Y-system
• Hexagon functions and the three-loop remainder function
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• From correlation functions to Wilson loops
• The super-correlator/super-amplitude duality: Part I
• From correlation functions to scattering amplitudes
• Analytic two-loop form factors in N=4 SYM
• 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
• Exciting the GKP string at any coupling
• More on the duality correlators/amplitudes
• OPE for all Helicity Amplitudes
• The super-correlator/super-amplitude duality: Part II
• The last of the simple remainders
• Renormalization group coefficients and the S-matrix
• Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling
• OPE for all Helicity Amplitudes II. Form Factors and Data Analysis
• Nonsinglet pentagons and NMHV amplitudes
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• Fermionic pentagons and NMHV hexagon
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders
• 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
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Implications of nonplanar dual conformal symmetry
• Dual conformal invariance for form factors
• Matrix pentagons
• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• Colour-Twist Operators I: Spectrum and Wave Functions
• An Operator Product Expansion for Form Factors II. Born level

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• New relations for tree-level form factors and scattering amplitudes
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
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• An Operator Product Expansion for Form Factors II. Born level
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations