Supersymmetric Yang-Mills Fields as an Integrable System and Connections with Other Non-Linear Systems

Abstract

Integrable properties, i.e. existence of linear systems, infinite number of conservation laws, Riemann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Backlund transformations, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N⩾3 these constraint equations give equations of motion of the fields, thus integrating the constraint equations is equivalent to integrate the equation of motion. Further, these equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. Therefore, these understandings also provide a possible method to solve the fullKeywordsConstraint EquationVertex OperatorChiral ModelElectroweak TheoryChiral FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.