Vortex Holography

TL;DR

This paper demonstrates vortex line solutions in AdS4 spacetime, showing their gravitational effects and dual field theory implications via the AdS/CFT correspondence, extending flat spacetime vortex models.

Contribution

It introduces vortex solutions in AdS4, analyzes their gravitational effects, and links their properties to boundary field theory correlators.

Findings

Vortex solutions exist in AdS4 with cylindrical symmetry.

Vortices induce a proportional deficit angle in spacetime.

The vortex mass density relates to boundary correlation function discontinuities.

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.