Integrability in Theories with Local U(1) Gauge Symmetry

Details Integrability in Theories with Local U(1) Gauge Symmetry Integrability in Theories with Local U(1) Gauge Symmetry

2007-02-13

arxiv.org/abs/hep-th/0702100v2

J.Phys.A40:9079-9088,2007

Physics

High Energy Physics

High Energy Physics - Theory

corrected typos, version accepted in J. Phys. A

Scientific paper

10.1088/1751-8113/40/30/027

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.

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