Cheshire charge and magnetic current on Alice strings from continuous solutions to the Yang-Mills equations.

Abstract

We formulate the theory of Alice strings directly in terms of continuous solutions of the Yang-Mills equations, without introducing an explicitly discontinuous electric charge operator. Cheshire charge arises as the (gauge-noncovariant) charge density in charged gauge-boson fields around the string. In an appropriate gauge this becomes a thin charged sheet, giving the expected discontinuity in the electric field. By a gauge transformation the Cheshire charge of a loop can be replaced by Cheshire magnetic current density.