Topological first-order vortices in a gauged CP (2) model

Abstract

We study time-independent radially symmetric first-order solitons in a CP (2) model interacting with an Abelian gauge field whose dynamics is controlled by the usual Maxwell term. In this sense, we develop a consistent first-order framework verifying the existence of a well-defined lower bound for the corresponding energy. We saturate such a lower bound by focusing on those solutions satisfying a particular set of coupled first-order differential equations. We solve these equations numerically using appropriate boundary conditions giving rise to regular structures possessing finite-energy. We also comment the main features these configurations exhibit. Moreover, we highlight that, despite the different solutions we consider for an auxiliary function β (r) labeling the model (therefore splitting our investigation in two a priori distinct branches), all resulting scenarios engender the very same phenomenology, being physically equivalent.

SUSY Chern–Simons $\mathbb{CP}^N$ and baby Skyrme models and their BPS structures

“…which is in agreement with [25]. We can consider the Lagrangian as in (5.6) but replacing the Table II gives us the potential and the BPS equations.…”

“…Then, we apply these ideas to different gauged CP N models and compare our results, naturally obtained from SUSY, with previous results found in the literature. The gauged CP N models, specially the CP 1 and CP 2 models, were treated previously regarding their BPS structure [21][22][23][24][25][26][27], their SUSY solutions [28,29] or some generalized BPS models [30][31][32]. We will construct an N = 2 extension for the gauge formulation of the gauge CP N models with Chern-Simons term.…”

First-order solitons with internal structures in an extended Maxwell- CP(2) model

“…4 of the Ref. [9]). In particular, in view of the approximate expressions (42) and (43), one gets that, near r = 0, the energy density obeys…”

“…with k ∈ Z. However, it was also demonstrated in [9] that the field equations arising from these two a priori different cases simply mimic each other, the resulting contexts being then phenomenologically equivalent (at least regarding topological solitons at the classical level). In this sense, in the remainder of the present manuscript, we consider the case β(r) = β 1 only.…”

“…We firstly select the dielectric function G (χ) as its relevance lying on the fact that, for r = r 0 , the additional field χ(r) vanishes and the dielectric function G equals the unity: in this case, as we have argued in the beginning of the present Section, the resulting solutions mimic those ones previously studied in the context of a purely CP (2) model in the presence of the Maxwell term [9]. On the other hand, for r = r 0 , the presence of a nontrivial solution for χ(r) given by (33) is expected to change the shape of the corresponding first-order vortices in a new way.…”