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

Abstract

We have shown the existence of self-dual solitons in a type of generalized Chern-Simons baby Skyrme model where the generalized function (depending only in the Skyrme field) is coupled to the sigma-model term. The consistent implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism requires the generalizing function becomes the superpotential defining properly the selfdual potential. Thus, we have obtained a topological energy lower-bound (Bogomol'nyi bound) and the self-dual equations satisfied by the fields saturating such a bound. The Bogomol'nyi bound being proportional to the topological charge of the Skyrme field is quantized whereas the total magnetic flux is not. Such as expected in a Chern-Simons model the total magnetic flux and the total electrical charge are proportional to each other. Thus, by considering the superpotential a wellbehaved function in the whole target space we have shown the existence of three types of self-dual solutions: compacton solitons, soliton solutions whose tail decays following an exponential-law e −αr 2 (α > 0), and solitons having a power-law decay r −β (β > 0). The profiles of the two last solitons can exhibit a compactonlike behavior. The self-dual equations have been solved numerically and we have depicted the soliton profiles, commenting on the main characteristics exhibited by them.

Phase transitions in the logarithmic Maxwell O(3)-sigma model

“…We investigate the numerical solution of the BPS equations (25) and (26), using the interpolation method (for more details on the interpolation method for solving differential equations see Ref. [49]).…”

“…To obtain this entropic densities we consider the numerical vortex solutions of Eqs. (25) and Fig. 6 Configurational entropy density for the variable field of the vortex (26) in Eq.…”

“…Topological solutions of the gauged O(3)-sigma model have been extensively studied [11,[17][18][19][20][21][22]. In the Skyrme model [23,24], a gauge symmetry is required for the scale invariance of a O(3)-sigma model with the dynamics of the gauge field governed by Maxwell term [20,25].…”

Phase transitions in the logarithmic Maxwell O(3)-sigma model

“…Topological solutions of the gauged O(3)-sigma model have been extensively studied [11,[17][18][19][20][21][22]. In the Skyrme model [23,24], a gauge symmetry is required for the scale invariance of a O(3)-sigma model with the dynamics of the gauge field governed by Maxwell term [20,25].…”

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

“…On the other side, the existence of BPS structures in gauged baby Skyrme models including the Chern-Simons term also has been revealed by using supersymmetry techniques [48], specifically, these models possess N = 2 SUSY extension. The matching of the BPS structures arising via the direct use of the BPS technique and SUSY formalism in the Chern-Simons baby Skyrme model has been discussed in [33].…”