Holographic Global Vortices with Novel Boundary Conditions

The AdS/CFT correspondence has significantly impacted the study of strongly coupled systems, providing insights into various condensed matter phenomena through its holographic duality. This paper introduces an alternative approach to the breaking of the global $U(1)$ symmetry in the bulk in two asymptotically AdS spacetimes: AdS plus hard wall and AdS Blackbrane. We explore a $(3+1)$-dimensional bulk $U(1)$ symmetry-breaking phase vacuum within a global $U(1)$ ${\phi }^4$ field theory, without the gauge field present in prior models. We find the symmetry-breaking vacuum requires that the mass squared is proportional to the quartic coupling. We also investigate numerical solutions of topologically stable vortex strings extending into the bulk. We find evidence that the full UV expansion is dual to a point-like boundary excitation.