# The holographic non-abelian vortex

## TL;DR

This paper investigates a fully back-reacted non-abelian vortex in a holographic superconductor model, revealing its thermodynamic preference over abelian vortices and identifying gapless excitations localized on the vortex.

## Contribution

It introduces a new non-abelian vortex solution in holography with detailed thermodynamic analysis and excitation spectrum characterization.

## Key findings

- Non-abelian vortex has lower free energy than abelian vortex in certain regimes.
- The vortex hosts a gapless $ ext{CP}^1$ excitation on its world line.
- The solution models a topological defect in a finite-temperature conformal field theory.

## Abstract

We study a fully back-reacted non-abelian vortex solution in an extension of the holographic superconductor setup. The thermodynamic properties of the vortex are computed. We show that, in some regime of parameters, the non-abelian vortex solution has a lower free energy than a competing abelian vortex solution. The solution is dual to a finite-temperature perturbed conformal field theory with a topological defect, on which operators related to the Goldstone modes of a spontaneously broken symmetry are localized. We compute numerically the retarded Green function of these operators and we find, in the classical approximation in the bulk, a gapless $\mathbb{CP}^1$ excitation on the vortex world line.