We study global vortices coupled to (2+1) dimensional gravity with negative cosmological constant. We found nonsingular vortex solutions in φ 4 -theory with a broken U(1) symmetry, of which the spacetimes do not involve physical curvature singularity. When the magnitude of negative cosmological constant is larger than a critical value at a given symmetry breaking scale, the spacetime structure is a regular hyperbola, however it becomes a charged black hole when the magnitude of cosmological constant is less than the critical value. We explain through duality transformation the reason why static global vortex which is electrically neutral forms black hole with electric charge. Under the present experimental bound of the cosmological constant, implications on cosmology as a straight black cosmic string is also discussed in comparison with global U(1) cosmic string in the spacetime of the zero cosmological constant.

The low energy dynamics of vortices in selfdual Abelian Higgs theory is of second order in vortex velocity and characterized by the moduli space metric. When Chern-Simons term with small coefficient is added to the theory, we show that a term linear in vortex velocity appears and can be consistently added to the second order expression. We provides an additional check of the first and second order terms by studying the angular momentum in the field theory. We briefly explore other first order term due to small background electric charge density and also the harmonic potential well for vortices given by the moment of inertia. * Electronic

The Abelian Higgs model with or without external particles is considered in curved space. Using the dual transformation, we rewrite the model in terms of dual gauge fields and derive the Bogomol'nyi-type bound. We find all possible cylindrically symmetric vortex solutions and vortex-particle composites by examining the Einstein equations and the firstorder Bogomol'nyi equations. The underlying spatial manifold of these objects comprises a cylinder asymptotically and a two sphere in addition to the well-known cone.