Integrability in Theories with Local U(1) Gauge Symmetry

TL;DR

This paper explores the integrability properties of the Abelian Higgs model with U(1) gauge symmetry, identifying integrable sectors and conserved currents using a generalized zero curvature approach.

Contribution

It introduces a gauge-invariant framework for understanding integrability in models with U(1) symmetry, extending the zero curvature method to new sectors.

Findings

Existence of integrable sectors with infinite conserved currents

Gauge-invariant description of weak and strong integrable sectors

Infinite conserved currents in Bogomolny configurations

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.