Exploring straight infinite Wilson lines in the Self Dual and the MHV Lagrangians

Abstract

We investigate the appearance of straight infinite Wilson lines lying on the self-dual plane in the context of the Self Dual sector of the Yang Mills theory and in a connection to the Lagrangian implementing the MHV vertices (MHV Lagrangian) according to the Cachazo-Svrcek-Witten method. It was already recognized in the past by two of the authors, that such Wilson line functional provides the field transformation of positive helicity fields between the Yang-Mills theory on the light-cone and the MHV Lagrangian. Here we discuss in detail the connection to the Self Dual sector and we provide a new insight into the solution for the minus helicity field transformation, which can be expressed in terms of a functional derivative of the straight infinite Wilson line on the self-dual plane.

arXiv comment26 pages, 3 figures

References in corpus (35)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• MHV Vertices And Tree Amplitudes In Gauge Theory
• The Amplituhedron
• High-Energy Factorization and Small-X Deep Inelastic Scattering Beyond Leading Order
• On-Shell Methods in Perturbative QCD
• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• The Kinematic Algebra From the Self-Dual Sector
• A direct proof of the CSW rules
• The self-dual sector of QCD amplitudes
• Feynman rules for effective Regge action
• Basics of Generalized Unitarity
• Asymmetries in Heavy Quark Pair and Dijet Production at an EIC
• On amplitudes in self-dual sector of Yang-Mills theory
• Helicity amplitudes for high-energy scattering
• The Lagrangian origin of MHV rules
• Self-dual Yang--Mills Theory and One-Loop Maximally Helicity Violating Multi-Gluon Amplitudes
• Exact kinematics in the small x evolution of the color dipole and gluon cascade
• Multi-gluon helicity amplitudes with one off-shell leg within high energy factorization
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• One-loop MHV Rules and Pure Yang-Mills
• Structure of the MHV-rules Lagrangian
• Wilson lines and gauge invariant off-shell amplitudes
• BCFW recursion for off-shell gluons
• Amplitudes in Pure Yang-Mills and MHV Diagrams
• On Soft Theorems And Form Factors In N=4 SYM Theory
• S-Matrix Equivalence Theorem Evasion and Dimensional Regularisation with the Canonical MHV Lagrangian
• MHV Lagrangian for N=4 Super Yang-Mills
• The MHV QCD Lagrangian
• Recursion relations for multi-gluon off-shell amplitudes on the light-front and Wilson lines
• Wilson lines in the MHV action
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• MHV One-Loop Amplitudes in Yang-Mills from Generalised Unitarity

Cited by in corpus (3)

• A new Wilson line-based action for gluodynamics
• One-Loop Effective Action Approach to Quantum MHV Theory
• Wilson Lines and Boundary Operators of BCFW Shifts