Self-dual solitons in a Maxwell-Chern-Simons baby Skyrme model

Abstract

We have studied the existence de self-dual solitons in a gauged version of the baby Skyrme model in which the gauge field dynamics is governed by the Maxwell-Chern-Simons action. For such a purpose, we have developed a detailed implementation of the Bogomol'nyi-Prasad-Sommerfield formalism providing the self-dual equations whose solutions saturate the energy lower bound. Such a bound related to the topological charge of the Skyrme field becomes quantized whereas both the total magnetic flux and the total electrical charge are not. We have found two types of self-dual Skyrme field profiles: the first is described by a solution which decays following an exponential-law (e −αr 2 , α > 0); the second is portrayed by a solution having a power-law decay (r −β , β > 0). On other hand, in both cases the asymptotic behavior of the gauge field is similar to the one presented in the context of the Abelian Higgs models describing Abrikosov-Nielsen-Olesen charged vortices. Other interesting feature we highlight is the localized magnetic flux inversion, a property does not observed in others gauged baby Skyrme models already studied in literature. Numerical results are presented for rotationally symmetrical field configurations by remarking some of its essential features.

Self-dual solitons in a generalized Chern-Simons baby Skyrme model

“…On the other hand, in [18][19][20] were studied the BPS configurations (carrying magnetic flux alone) in the restricted gauge baby Skyrme model. Moreover, in [21][22][23] is analyzed the self-dual solutions carrying both the magnetic flux and electric charge. It is essential to point out the restricted gauged baby Skyrme model also allows a supersymmetric extension [24][25][26][27][28].…”

Ringlike vortices in a logarithmic generalized Maxwell theory

“…at the BPS limit we will obtain vortex structures with energy described by the equation (18). In this way, the BPS equations are reduced to We recall that the magnetic field and the energy can be obtained by analyzing eq.…”

“…Study of planar structures like vortex has been investigated since the beginning of the theory proposed by Bogomol'nyi-Prasad-Sommerfield [1,[17][18][19]. However, in recent years, these planar structures have been investigated in generalized models such as [20,21].…”

Solitons in the gauged Skyrme-Maxwell model

“…Furthermore, electrically charged planar Skyrmions were studied is an extended model with a Chern-Simons term [63][64][65]. The gauged BPS baby-Skyrme model was considered recently in [66,67]. Interesting examples of gauged topological solitons were also constructed in the O(3) sigma model [59], and in the U (1) gauged Faddeev-Skyrme-Maxwell theory [68,69].…”