Conformal properties of four-gluon planar amplitudes and Wilson loops

Abstract

We present further evidence for a dual conformal symmetry in the four-gluon planar scattering amplitude in N=4 SYM. We show that all the momentum integrals appearing in the perturbative on-shell calculations up to five loops are dual to true conformal integrals, well defined off shell. Assuming that the complete off-shell amplitude has this dual conformal symmetry and using the basic properties of factorization of infrared divergences, we derive the special form of the finite remainder previously found at weak coupling and recently reproduced at strong coupling by AdS/CFT. We show that the same finite term appears in a weak coupling calculation of a Wilson loop whose contour consists of four light-like segments associated with the gluon momenta. We also demonstrate that, due to the special form of the finite remainder, the asymptotic Regge limit of the four-gluon amplitude coincides with the exact expression evaluated for arbitrary values of the Mandelstam variables.

25 pages, 6 figures; v3: minor corrections, references added

References in corpus (8)

• Gluon scattering amplitudes at strong coupling
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Iterative Structure Within The Five-Particle Two-Loop Amplitude

Cited by in corpus (60)

• New Relations for Gauge-Theory Amplitudes
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• All tree-level amplitudes in N=4 SYM
• Spinning strings at one-loop in AdS_4 x P^3
• Exacting N=4 Superconformal Symmetry
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Generating AdS String Solutions
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Integrability of scattering amplitudes in N=4 SUSY
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• Iterated amplitudes in the high-energy limit
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Tree-Level Amplitudes in N=8 Supergravity
• New Dual Conformally Invariant Off-Shell Integrals
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Some properties of the Alday-Maldacena minimum
• Conformal invariance from non-conformal gravity
• Is it possible to check urgently the 5-loop analytical results for the $e^{+}{e}^{-}$-annihilation Adler function ?
• Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations
• Gluon scattering in $\mathcal{N}=4$ Super Yang-Mills at finite temperature
• A super MHV vertex expansion for N=4 SYM theory
• Lectures on Scattering Amplitudes via AdS/CFT
• Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II. Polygons which admit an inscribed circle
• Gluon Scattering in Deformed N=4 SYM
• Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD
• First-quantized N=4 Yang-Mills
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time
• Infrared Safe Observables in $\mathcal{N}=4$ Super Yang-Mills Theory
• "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle
• Supersymmetric Wilson Loops in Diverse Dimensions
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• Matching gluon scattering amplitudes and Wilson loops in off-shell regularization
• Twistors, strings and supersymmetric gauge theories
• Universal structure of subleading infrared poles at strong coupling
• A Note on Loop Amplitudes in QED
• Algebra of Lax Connection for T-Dual Models
• Theoretical Developments in SUSY
• MHV amplitudes, Wilson loops and the BDS ansatz in the superconformal N=2 QCD
• Topics in Cusped/Lightcone Wilson Loops