  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.
