Quantum field theory of non-abelian strings and vortices

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.