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.

7 pages, 5 figures. v2: references added, convention changed

References in corpus (14)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• 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
• 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
• Renormalization group coefficients and the S-matrix
• The last of the simple remainders
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Colour-Twist Operators I: Spectrum and Wave Functions
• An Operator Product Expansion for Form Factors II. Born level

Cited by in corpus (25)

• Cluster algebras for Feynman integrals
• A Three-Point Form Factor Through Five Loops
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Antipodal Self-Duality for a Four-Particle Form Factor
• Three-point energy correlator in $\mathcal{N}=4$ super Yang-Mills Theory
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• First look at the evaluation of three-loop non-planar Feynman diagrams for Higgs plus jet production
• Full-color three-loop three-point form factors in N=4 SYM
• Bootstrapping a Two-Loop Four-Point Form Factor
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• The Four-Loop $\mathcal{N}=4$ SYM Sudakov Form Factor
• Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• A Two-Loop Four-Point Form Factor at Function Level
• 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
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• 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