On spinors, strings, integrable models and decomposed Yang-Mills theory

Abstract

This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three dimensional string-like structures. Then its relation to the structure of the su(2) Lie algebra valued Maurer-Cartan one-form is presented; while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is show how the Lax pair of the integrable nonlinear Schroedinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation and it is described how a spinor based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schroedinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauss-Godazzi equation that describes surfaces in three dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two dimensional and four dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two dimensional integrable models as embedded structures in the four dimensional decomposed SU(2) Yang-Mills theory are presented.

References in corpus (17)

• Partially Dual variables in SU(2) Yang-Mills Theory
• Hidden symmetry and knot solitons in a charged two-condensate Bose system
• MacDowell-Mansouri gravity and Cartan geometry
• The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins
• Isothermic surfaces in $\E^3$ as soliton surfaces
• Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory
• Decomposing the Yang-Mills Field
• Discrete Nonlinear Schrodinger Equation, Solitons and Organizing Principles for Protein Folding
• Integrability of Vortex Equations on Riemann Surfaces
• A Gauge Field Theory of Chirally Folded Homopolymers with Applications to Folded Proteins
• Phases of bosonic strings and two dimensional gauge theories
• Non-Abelian Supercurrents and de Sitter Ground State in Electroweak Theory
• Integrable vortex-type equations on the two-sphere
• On Energy Functions for String-Like Continuous Curves, Discrete Chains, and Space-Filling One Dimensional Structures
• Vortices on Hyperbolic Surfaces
• Vortex solutions of the Popov equations
• Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions

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