Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space

Abstract

We study a complex analogue of a Wilson Loop, defined over a complex curve, in non-Abelian holomorphic Chern-Simons theory. We obtain a version of the Makeenko-Migdal loop equation describing how the expectation value of these Wilson Loops varies as one moves around in a holomorphic family of curves. We use this to prove (at the level of the integrand) the duality between the twistor Wilson Loop and the all-loop planar S-matrix of N=4 super Yang-Mills by showing that, for a particular family of curves corresponding to piecewise null polygons in space-time, the loop equation reduce to the all-loop extension of the BCFW recursion relations. The scattering amplitude may be interpreted in terms of holomorphic linking of the curve in twistor space, while the BCFW relations themselves are revealed as a holomorphic analogue of skein relations.

29 pages, 6 figures

References in corpus (13)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Gluon scattering amplitudes at strong coupling
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• Scattering into the fifth dimension of N=4 super Yang-Mills
• New differential equations for on-shell loop integrals
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• MHV Diagrams in Momentum Twistor Space
• MHV Diagrams from an All-Line Recursion Relation
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes

Cited by in corpus (21)

• The super-correlator/super-amplitude duality: Part I
• Scattering Amplitudes and Wilson Loops in Twistor Space
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• MHV diagrams in twistor space and the twistor action
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• From the Holomorphic Wilson Loop to `d log' Loop-Integrands of Super-Yang-Mills Amplitudes
• Descent equations for superamplitudes
• Amplitudes of 3d Yang Mills Theory
• Correlation functions, null polygonal Wilson loops, and local operators
• From Polygon Wilson Loops to Spin Chains and Back
• Multichannel Conformal Blocks for Polygon Wilson Loops
• Gluon scattering on self-dual radiative gauge fields
• Twistor actions for gauge theory and gravity
• Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
• Minitwistors and 3d Yang-Mills-Higgs theory
• On the Geometry of Null Polygons in Full N=4 Superspace
• Weak Coupling, Degeneration and Log Calabi-Yau Spaces
• Loop space and evolution of the light-like Wilson polygons
• Wilson Loop Form Factors: A New Duality
• Twistors, Harmonics and Holomorphic Chern-Simons
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes