Are scattering amplitudes dual to super Wilson loops?

Abstract

The MHV scattering amplitudes in planar N=4 SYM are dual to bosonic light-like Wilson loops. We explore various proposals for extending this duality to generic non-MHV amplitudes. The corresponding dual object should have the same symmetries as the scattering amplitudes and be invariant to all loops under the chiral half of the N=4 superconformal symmetry. We analyze the recently introduced supersymmetric extensions of the light-like Wilson loop (formulated in Minkowski space-time) and demonstrate that they have the required symmetry properties at the classical level only, up to terms proportional to field equations of motion. At the quantum level, due to the specific light-cone singularities of the Wilson loop, the equations of motion produce a nontrivial finite contribution which breaks some of the classical symmetries. As a result, the quantum corrections violate the chiral supersymmetry already at one loop, thus invalidating the conjectured duality between Wilson loops and non-MHV scattering amplitudes. We compute the corresponding anomaly to one loop and solve the supersymmetric Ward identity to find the complete expression for the rectangular Wilson loop at leading order in the coupling constant. We also demonstrate that this result is consistent with conformal Ward identities by independently evaluating corresponding one-loop conformal anomaly.

25 pages; v2: minor corrections, a new appendix with discussion of conformal anomaly is added

References in corpus (16)

• Gluon scattering amplitudes at strong coupling
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• The super-correlator/super-amplitude duality: Part I
• From correlation functions to scattering amplitudes
• More on the duality correlators/amplitudes
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• On BCFW shifts of integrands and integrals
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory

Cited by in corpus (53)

• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• 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
• Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
• More on the duality correlators/amplitudes
• Scattering Amplitudes and Wilson Loops in Twistor Space
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• Nonsinglet pentagons and NMHV amplitudes
• Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Fermionic pentagons and NMHV hexagon
• One Loop Amplitudes In ABJM
• Quantum mechanics of null polygonal Wilson loops
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• Dual Conformal Structure Beyond the Planar Limit
• Descent equations for superamplitudes
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• On factorization of multiparticle pentagons
• From Polygon Wilson Loops to Spin Chains and Back
• Correlation functions, null polygonal Wilson loops, and local operators
• Multichannel Conformal Blocks for Polygon Wilson Loops
• All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
• Wilson Loops @ 3-Loops in Special Kinematics
• OPE for null Wilson loops and open spin chains
• Twistor actions for gauge theory and gravity
• Null Polygonal Wilson Loops in Full N=4 Superspace
• χ-Systems for Correlation Functions
• Nonperturbative enhancement of superloop at strong coupling
• Conformal anomaly of super Wilson loop
• Towards NMHV amplitudes at strong coupling
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Dual conformal symmetry on the light-cone
• On the Geometry of Null Polygons in Full N=4 Superspace
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• Multichannel conformal blocks for scattering amplitudes
• Yangian Symmetry in N=4 super Yang-Mills
• Resummed tree heptagon
• Supersymmetric quantum mechanics of the flux tube
• A note on two-loop superloop
• Supersymmetric Wilson Loops via Integral Forms
• Superpropagator and superconformal invariants
• Descent equation for superloop and cyclicity of OPE
• Wilson Loop Form Factors: A New Duality
• Vertex Operators of Super Wilson Loops
• Super Wilson Loops and Holonomy on Supermanifolds
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• The Twofold Way of Super Holonomy
• Asymptotic behavior of large polygonal Wilson loops in confining gauge theories