Solitons in a baby-Skyrme model with invariance under area-preserving diffeomorphisms

Abstract

We study the properties of soliton solutions in an analogue of the Skyrme model in 2ϩ1 dimensions whose Lagrangian contains the Skyrme term and the mass term, but no usual kinetic term. The model admits a symmetry under area-preserving diffeomorphisms. We solve the dynamical equations of motion analytically for the case of spinning isolated baryon-type solitons. We take fully into account the induced deformation of the spinning Skyrmions and the consequent modification of its moment of inertia to give an analytical example of related numerical behavior found by Piette, Schroers, and Zakrzewski. We solve the equations of motion also for the case of an infinite, open string, and a closed annular string. In each case, the solitons are of finite extent, so called ''compactons,'' being exactly the vacuum outside a compact region. We end with indications on the scattering of baby Skyrmions, as well as some considerations as the properties of solitons on a curved space. ͓S0556-2821͑97͒03512-1͔

Magnetothermodynamics of BPS baby skyrmions

“…It has been previously found that the model preserves many properties of the original ungauged version [41][42][43]. First of all, there is a BPS bound which can be saturated by the corresponding BPS configurations.…”

“…In fact, there exists a (2 + 1) dimensional version of the Skyrme model, usually referred to as the baby Skyrme model, which supports solitonic solutions (baby skyrmions) [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] (for the gauged version see [39,40]). This field theory also possesses its BPS limit, whose Lagrangian consists of the (2+1) dimensional version of the Skyrme term and a potential [41][42][43]. Moreover, there is again a gauged version of this model, the so-called gauged BPS baby Skyrme model, which has been analyzed recently in the case of an asymptotically vanishing magnetic field [44].…”

Extended supersymmetry and BPS solutions in baby Skyrme models

“…Concretely, in a first step we derive the equation for one-half BPS states for a completely general N = 2 chiral superfield. Then we apply the resulting equation to the SUSY BPS baby Skyrme model and find that its one-half BPS states are precisely the BPS solutions of the BPS baby Skyrme model [37]- [40]. In section 9 we introduce the N = 2 SUSY extension of the gauged baby Skyrme model.…”

“…In addition, in both models the energies of static configurations can be bound from below by a Bogomol'nyi bound (a multiple of the topological degree), but generic soliton solutions do not saturate this bound. It is, however, possible both for the baby Skyrme model [37]- [40] and for a generalized Skyrme model [41]- [45] (i.e., a generalization of the original model proposed by Skyrme) to find certain submodels such that their topological soliton solutions saturate the corresponding Bogomol'nyi bound, that is, they are of the BPS type and obey certain first-order BPS equations.…”

Volume of a vortex and the Bradlow bound

“…ð4:29Þ which is closely related to the so-called BPS baby Skyrme model [27][28][29][30]. It consists of two parts, a fourth derivative term which has a vacuum at juj ¼ 1.…”