We develop an operator formalism for investigating the properties of non-abelian cosmic strings (and vortices) in quantum field theory. Operators are constructed that introduce classical string sources and that create dynamical string loops. The operator construction in lattice gauge theory is explicitly described, and correlation functions are computed in the strong-coupling and weak-coupling limits. These correlation functions are used to study the long-range interactions of non-abelian strings, taking account of charge-screening effects due to virtual particles. Among the phenomena investigated are the Aharonov-Bohm interactions of strings with charged particles, holonomy interactions between string loops, string entanglement, the transfer of "Cheshire charge" to a string loop, and domain-wall decay via spontaneous string nucleation. We also analyze the Aharonov-Bohm interactions of magnetic monopoles with electric flux tubes in a confining gauge theory. We propose that the Aharonov-Bohm effect can be invoked to distinguish among various phases of a non-abelian gauge theory coupled to matter.

We analyze the charges carried by loops of string in models with non-abelian local discrete symmetry. The charge on a loop has no localized source, but can be detected by means of the Aharonov-Bohm interaction of the loop with another string. We describe the process of charge detection, and the transfer of charge between point particles and string loops, in terms of gauge-invariant correlation functions.

We consider the topological interactions of vortices on general surfaces. If the genus of the surface is greater than zero, the handles can carry magnetic flux. The classical state of the vortices and the handles can be described by a mapping from the fundamental group to the unbroken gauge group. The allowed configurations must satisfy a relation induced by the fundamental group. Upon quantization, the handles can carry "Cheshire charge." The motion of the vortices can be described by the braid group of the surface. How the motion of the vortices affects the state is analyzed in detail.

The electric charge of a wormhole mouth and the magnetic flux "linked" by the wormhole are non-commuting observables, and so cannot be simultaneously diagonalized. We use this observation to resolve some puzzles in wormhole electrodynamics and chromodynamics. Specifically, we analyze the color electric field that results when a colored object traverses a wormhole, and we discuss the measurement of the wormhole charge and flux using Aharonov-Bohm interference effects. We suggest that wormhole mouths may obey conventional quantum statistics, contrary to a recent proposal by Strominger.

In this letter we show how string winding modes can be constructed using topological membranes. We use the fact that monopole-instantons in compact topologically massive gauge theory lead to charge non-conservation inside the membrane which, in turn, enables us to construct vertex operators with different left and right momenta. The amount of charge non-conservation inside the membrane is interpreted as giving the momentum associated with the string winding mode and is shown to match precisely the full mass spectrum of compactified string theory. * leith@thphys.ox.ac.uk