Topological approach to Alice electrodynamics

In a spontaneously broken non-abelian gauge theory, charge conjugation can be a local symmetry. That is, the unbroken gauge group H may contain both a U(1) factor generated by Q, and an element X of the disconnected component of H such that XQX ‘= — Q. Such a model contains topologically-stable cosmic strings with a remarkable property — when a charged particle is transported around the string, the sign of its charge flips. (The sign of the charge is gauge dependent, but the feature that the sign changes has an unambiguous and gauge-invariant meaning.) This string, which acts as a charge-conjugation looking glass, was first discussed by A.S. Schwarz, who dubbed it the “Alice” string [1]. (The possibility that charge conjugation could be a local symmetry was noted earlier by Kiskis [2].) A closed loop of Alice string can carry electric charge, and the charge lost by a particle that winds around the string is transferred to the loop. A charged string loop is a peculiar object. It has a long-range electric field, from which its charge can be inferred, yet there is no localized source of charge anywhere on the string or in its vicinity [3—5].Such charge with no locally identifiable source has been called “Cheshire charge” [4]. An Alice string can also carry magnetic Cheshire charge, and can exchange magnetic charge with magnetic monopoles [3,6,7]. The properties of Alice strings that carry Cheshire charge, and the processes by which charge is exchanged between strings and point particles, have been analyzed