Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory

Abstract

We study the form factor of a generic gauge-invariant local composite operator in $\mathcal{N}=4$ SYM theory. At tree level and for a minimal number of external on-shell super fields, we find that the form factor precisely yields the spin-chain picture of integrability in the language of scattering amplitudes. Moreover, we compute the cut-constructible part of the one-loop correction to this minimal form factor via generalised unitarity. From its UV divergence, we obtain the complete one-loop dilatation operator of $\mathcal{N}=4$ SYM theory. Thus, we provide a field-theoretic derivation of a relation between the one-loop dilatation operator and the four-point tree-level amplitude which was observed earlier. We also comment on the implications of our findings in the context of integrability.

arXiv comment39 pages, several figures, feynmp; v2: references added, typos corrected; v3: references added, typos corrected, one explanation improved, matches published version

References in corpus (53)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• 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
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Review of AdS/CFT Integrability: An Overview
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• The N=4 SYM Integrable Super Spin Chain
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• MHV Vertices And Tree Amplitudes In Gauge Theory
• What is the Simplest Quantum Field Theory?
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Comments on gluon scattering amplitudes via AdS/CFT
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Space-time S-matrix and Flux-tube S-matrix at Finite Coupling
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• On-Shell Methods in Perturbative QCD
• Factorization in One-Loop Gauge Theory
• Tailoring Three-Point Functions and Integrability
• Form factors at strong coupling via a Y-system
• All tree-level amplitudes in N=4 SYM
• Color-kinematic Duality for Form Factors
• Analytic two-loop form factors in N=4 SYM
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• Harmony of Super Form Factors
• On form factors in N=4 sym
• The three-loop form factor in N=4 super Yang-Mills
• Wrapping interactions and the genus expansion of the 2-point function of composite operators
• The last of the simple remainders
• From multiple unitarity cuts to the coproduct of Feynman integrals
• Harmonic R-matrices for Scattering Amplitudes and Spectral Regularization
• HHL correlators, orbit averaging and form factors
• On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory
• Yang-Baxter operators and scattering amplitudes in $\mathcal{N}=4$ super-Yang-Mills theory
• Spectral Parameters for Scattering Amplitudes in N=4 Super Yang-Mills Theory
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• On super form factors of half-BPS operators in N=4 super Yang-Mills
• Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• On Form Factors in N=4 SYM Theory and Polytopes
• N=4 Scattering Amplitudes and the Deformed Grassmannian
• A dictionary between R-operators, on-shell graphs and Yangian algebras
• A Twistorial Approach to Integrability in N=4 SYM
• Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
• Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory

Cited by in corpus (38)

• Lectures on Yangian Symmetry
• Structure of two-loop SMEFT anomalous dimensions via on-shell methods
• Renormalization group coefficients and the S-matrix
• A Three-Point Form Factor Through Five Loops
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders
• Master integrals for the four-loop Sudakov form factor
• The SU(2|3) dynamic two-loop form factors
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• An Operator Product Expansion for Form Factors
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• A note on connected formula for form factors
• On Soft Theorems And Form Factors In N=4 SYM Theory
• Full-color three-loop three-point form factors in N=4 SYM
• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
• On Form Factors and Correlation Functions in Twistor Space
• Grassmannians and form factors with $q^2=0$ in N=4 SYM theory
• Wilson lines, Grassmannians and Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Form Factor and Boundary Contribution of Amplitude
• Integrability and unitarity
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• The all-loop conjecture for integrands of reggeon amplitudes in N=4 SYM
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• Gluonic evanescent operators: classification and one-loop renormalization
• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• ALPs, the on-shell way
• The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve
• On Yangian symmetry of scattering amplitudes and the dilatation operator in N=4 super Yang-Mills
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• An Operator Product Expansion for Form Factors II. Born level
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons