Vortex Holography

Abstract

We show that the Abelian Higgs field equations in the four dimensional anti de Sitter spacetime have a vortex line solution. This solution, which has cylindrical symmetry in AdS$_4$, is a generalization of the flat spacetime Nielsen-Olesen string. We show that the vortex induces a deficit angle in the AdS$_4$ spacetime that is proportional to its mass density. Using the AdS/CFT correspondence, we show that the mass density of the string is uniform and dual to the discontinuity of a logarithmic derivative of correlation function of the boundary scalar operator.