Baryonic handles: Skyrmions as open vortex strings on a domain wall

Abstract

We consider the BEC-Skyrme model which is based on a Skyrme-type model with a potential motivated by Bose-Einstein condensates (BECs) and, in particular, we study the Skyrmions in proximity of a domain wall that inhabits the theory. The theory turns out to have a rich flora of Skyrmion solutions that manifest themselves as twisted vortex rings or vortons in the bulk and vortex handles attached to the domain wall. The latter are linked open vortex strings. We further study the interaction between the domain wall and the Skyrmion and between the vortex handles themselves as well as between the vortex handle and the vortex ring in the bulk. We find that the domain wall provides a large binding energy for the solitons and it is energetically preferred to stay as close to the domain wall as possible; other configurations sticking into the bulk are metastable.We find that the most stable 2-Skyrmion is a torus-shaped braided string junction ending on the domain wall, which is produced by a collision of two vortex handles on the wall, but there is also a metastable configuration which is a doubly twisted vortex handle produced by a collision of a vortex handle on the wall and a vortex ring from the bulk.

Linking number of vortices as baryon number

“…For the positive sign, there are two vacua: ψ = (e iα , 0) and (0, e iα ) [10][11][12][13], while for the negative sign the vacuum is: S 1 × S 1 , |ψ 1 | 2 = |ψ 2 | 2 = 1/2. In the former case, the situation is similar to that of the potential (3.2) admitting physical vortex zeros and vacuum vortex zeros, while in the latter case both zeros can be physical vortices.…”

Linked vortices as baryons in the miscible BEC-Skyrme model

“…Similar vortex rings can also be obtained in a different asymmetric potential, V ∼ M 2 jϕ 1 j 2 [26]. In addition to a vortex ring, the BECinspired potential also allows for a domain wall [22][23][24] into which the vortex ring can be absorbed, creating a vortex handle-or rather a link of a handle and a dual handle from both sides of the domain wall [27]. We would like to stress that the Skyrmions we study here are closer to those describing nuclei within the Skyrme model, than to the Skyrmions in BEC, because of the derivative part of the Lagrangian.…”

“…The two seemingly different vortices were always present at the same time and hence topologically the immiscible BECinspired potential of Ref. [27] gives rise to a symmetry breaking supporting only one topological number for the vortices. In principle, in this model we can have two independent numbers of vortices.…”

“…The immiscible BEC-Skyrme model was shown to contain vortex rings in Ref. [27] and when pushed toward a domain wallpresent for the immiscible BEC-inspired potential-the vortex ring turned into a handle (in say ϕ 1 ) on the domain wall, albeit creating a second dual handle (in ϕ 2 ). The two seemingly different vortices were always present at the same time and hence topologically the immiscible BECinspired potential of Ref.…”

“…In this paper, we modify the BEC-inspired potential studied in Refs. [22][23][24]27] by flipping the sign of the potential (which is allowed in a nonlinear sigma model) and this is suitable for the class of BECs called miscible twocomponent BECs, for which both the components ϕ 1 and ϕ 2 develop vacuum expectation values (VEVs) in the vacua. The implications thereof is a rather crucial change in the vacuum structure and indeed the model only possesses a unique vacuum state after the altercation, which we dub the miscible BEC-Skyrme model.…”