Solitonic vortices and black holes with vortex hair in AdS$_3$

TL;DR

This paper explores soliton and black hole solutions with scalar hair in AdS$_3$, revealing complex phase transitions and vortex phenomena relevant to holographic superconductors and dual boundary theories.

Contribution

It introduces new black hole and soliton solutions with vortex hair in AdS$_3$, analyzing their phase diagram and transition behaviors under double trace boundary conditions.

Findings

Identified phase transitions of Hawking-Page and condensation types.

Discovered a transition between vortex solutions and zero-temperature black holes.

Observed Little-Park periodicity in the dual boundary theory.

Abstract

We study soliton and black hole solutions with scalar hair in AdS$_3$ in a theory with a Maxwell field and a charged scalar field with double trace boundary conditions, which can trigger the dual boundary theory to become a superconductor. We investigate the phase diagram as a function of the temperature $T$ and of the double trace coupling $\kappa$ and we find a rich pattern of phase transitions, which can be of the Hawking-Page kind or can be due to the condensation of the order parameter. We also find a transition between vortex solutions and the zero temperature limit of the black hole for a critical value of the double trace coupling $\kappa$. The Little-Park periodicity is realized for the dual of the black hole solution with hair as a shift in the winding number and in the gauge field.