2020/06/29 by Hiren Kakkad, Piotr Kotko, Anna Staśto +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Connection (principal bundle) #Context (archaeology) #Dual (grammatical number) #Field (mathematics) #Field theory (psychology) #Geometry #Helicity #Lagrangian #Line (geometry) #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Philosophy #Physics #Plane (geometry) #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Transformation (genetics) #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.102.094026
26 pages, 3 figures
arxiv created 2020/06/29 · openalex publication_date 2020/11/30 · arxiv updated 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 maximally helicity violating (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.