Abstract
We study the interaction of a class of closed solitonic string states (“winders”) which wind around the Kaluza-Klein circle with a Kaluza-Klein monopole. We find that winders are attracted towards monopoles with an inverse-square law force and even when moving relativistically they pursue exactly elliptical parabolic or hyperbolic orbits. The simplicity of the motion is due to the existence of an extra conserved Runge-Lenz vector in addition to the conserved angular momentum. The Poisson algebra of these conserved vectors closes on so (3) ⊕ s R 3 or so (3), so (3) ⊕ s R or so (3) ⊕ so (2, 1). We also find a class of instanton solutions of the euclidean equations in the field of two or more monopoles. The possibility that monopoles catalyse the decay or annihilation of winders is discussed.
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