Exact vortex solutions in a CP^N Skyrme-Faddeev type model

TL;DR

This paper introduces an integrable sector in a generalized CP^N Skyrme-Faddeev model, providing exact vortex solutions with complex interactions, revealing new insights into soliton dynamics in four-dimensional field theories.

Contribution

It constructs an infinite class of exact solutions in a CP^N Skyrme-Faddeev type model, highlighting integrability and hidden symmetries in four-dimensional soliton configurations.

Findings

Existence of an integrable sector with infinite conservation laws

Construction of exact vortex solutions with wave interactions

Observation of intricate vortex and wave energy interactions

Abstract

We consider a four dimensional field theory with target space being CP^N which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP^1. We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x^1+i x^2) and (x^3+x^0) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.