Non-Abelian vortices in holographic superconductors

Abstract

We find, by an appropriate extension of the standard holographic superconductor setup, static bulk solutions which describe holographic duals to non-Abelian vortices. In the core of these vortices a scalar field condenses, breaking a non-Abelian global symmetry which leads to additional zero modes called orientational moduli. These moduli appear in the bulk as Goldstone bosons associated to the condensation of a neutral scalar field.

Multi-Skyrmions with orientational moduli

“…The case of non-Abelian vortices has been of particular interest as a possible description of the vortices responsible for the dual [20] [33]) in which orientational moduli can condense on solitonic solutions [25]. The model was recently used to construct the first case of non-Abelian vortices in holographic models at strong coupling [26]. The analysis shows that the main ingredients responsible for the presence of orientational moduli are: a) a bulk theory with a global non-Abelian symmetry G (which must be unbroken initially) and which admits topological defects uncharged under this symmetry (Skyrmions in the present case), b) the breaking of G down to a global subgroup H on the given defect.…”

Vortons with Abelian and non-Abelian currents and their stability

“…In this section we present numerical solutions to equations (18). To solve for specific vorton solutions we considered axially symmetric solutions on a two dimensional grid in the (r, z)-plane.…”

“…where F [f n ] are the equations of motion (18), and c is the learning parameter. We choose c to achieve convergence in the procedure (typically c ∼ 0.001 − 0.1).…”

“…The solutions were found using a standard Newton-Rhapson relaxation algorithm. As stated earlier the value of Q was held constant, while the system in (18) was solved at each iteration with ω determined in (16). In Figure 2 we show another solution which is a representative of what happens near to the thin vorton limit.…”

“…To determine the stability of the vorton under small perturbations of the χ 3 field we consider the effective potential for small χ 3 perturbations in the equations of motion. Following from (18) we have…”