First-order vortices in a gauged CP(2) model with a Chern-Simons term

Abstract

We consider a gauged CP (2) theory in the presence of the Chern-Simons action, focusing our attention on those time-independent solutions possessing radial symmetry. In this context, we develop a coherent first-order framework via the Bogomol'nyi prescription, from which we obtain the corresponding energy lower-bound and the first-order equations the model supports. We use these expressions to introduce effective BPS scenarios, solving the resulting first-order equations by means of the finite-difference scheme, this way attaining genuine field solutions engendering topological configurations. We depict the new profiles, commenting on the main properties they engender.

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

“…Again the specific choice ζ = − 1 4 and Q = 1 2 diag(1, −1, 0) reproduces the results of [26]. We can consider finally the Maxwell-Chern-Simons CP 2 model [27].…”

“…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.…”

BPS Maxwell-Chern-Simons vortices with internal structures: the Abelian Higgs and the gauged $CP(2)$ cases

“…Therefore, the system above stands for the first-order BPS equations of the model (also here, the upper (lower) sign holds for n > 0 (n < 0)). In particular, when these first-order equations are satisfied, the energy of the resulting BPS configurations is equal to E BP S , the corresponding Bogomol'nyi bound, calculated in (10).…”

“…More recently, based on the exploration of the phenomenological relation between the gauged CP (N ) and the 4D Yang-Mills models, Loginov [8] has shown the existence of vortex solutions in a Maxwell-CP (2) model. By following such an approach, some of us have obtained first-order vortices in a Maxwell-CP (2) [9], in a Chern-Simons-CP (2) [10] and also in a Maxwell-Chern-Simons-CP (2) [11] theories.…”

Maxwell-$CP(2)$ vortices in the presence of magnetic impurities

“…More recently, time-independent vortices were also studied in connection to a Maxwell-CP (2) model via the second-order Euler-Lagrange equations [8], from which some of us have verified the existence of their firstorder counterparts [9]. Rotationally symmetric configurations were also considered in the context of both the Chern-Simons-CP (2) [10] and the Maxwell-Chern-Simons-CP (2) [11] theories, these investigations being motivated by a close phenomenological relation between the gauged CP (N ) models and four-dimensional Yang-Mills theories.…”