Integrability in Theories with Local U(1) Gauge Symmetry

Abstract

Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable sectors, where integrability is understood as the existence of infinitely many conserved currents. In particular, a gauge invariant description of the weak and strong integrable sectors is provided. The pertinent integrability conditions are given by a U(1) generalization of the standard strong and weak constraints for models with two dimensional target space. The Bogomolny sector is discussed, as well, and we find that each Bogomolny configuration supports infinitely many conserved currents. Finally, other models with U(1) gauge symmetry are investigated.

arXiv commentcorrected typos, version accepted in J. Phys. A

References in corpus (19)

• Bogomol'nyi solitons in a gauged $O(3)$ sigma model
• A New Approach to Integrable Theories in any Dimension
• Asymptotic Interactions of Critically Coupled Vortices
• Static intervortex forces
• Integrability and Conformal Symmetry in Higher Dimensions: A Model with Exact Hopfion Solutions
• The dynamics of vortices on S^2 near the Bradlow limit
• Expansion for the solutions of the Bogomolny equations on the torus
• Infinite symmetries in the Skyrme model
• Expansion in the Width: the Case of Vortices
• Integrability from an abelian subgroup of the diffeomorphism group
• Integrable Chiral Theories in 2+1 Dimensions
• Integrable theories in any dimension and homogenous spaces
• More on scattering of Chern-Simons vortices
• Generalized integrability conditions and target space geometry
• New Integrable Sectors in Skyrme and 4-dimensional CP^n Model
• Conservation laws in Skyrme-type models
• Construction of exact Riemannian instanton solutions
• Symmetries of generalized soliton models and submodels on target space $S^2$
• Bogomolny equations for vortices in the noncommutative torus

Cited by in corpus (2)

• Integrable theories and loop spaces: fundamentals, applications and new developments
• Integrable subsystem of Yang--Mills dilaton theory