arXiv subjects

C. Naya

Publications and source records attributed to C. Naya.

21 records · Page 2Linked to original sources

arXiv2012

The vector BPS Skyrme model

We analyze the vector meson formulation of the BPS Skyrme model in (3+1) dimensions, where the term of sixth power in first derivatives characteristic for the original, integrable BPS Skyrme model (the topological or baryon current squared) is replaced by a coupling between the vector meson $ω_μ$ and the baryon current. We find that the model remains integrable in the sense of generalized integrability and almost solvable (reducible to a set of two first order ODEs) for any value of the baryon charge. Further, we analyze the appearance of topological solitons for two one-parameter families of one vacuum potentials: the old Skyrme potentials and the so-called BPS potentials. Depending on the value of the parameters we find several qualitatively different possibilities. In the massless case we have a parameter region with no skyrmions, a unique compact skyrmion with a discontinuous first derivative at the boundary (equivalently, with a source term located at the boundary, which screens the topological charge), and Coulomb-like localized solitons. For the massive vector meson, besides the no-skyrmion region and a unique C-compact soliton, we find exponentially as well as power-like localized skyrmions. Further, we find (for a specific potential) BPS solutions, i.e., skyrmions saturating a Bogomolny bound (both for the massless and massive vector mesons) which are unstable for higher values of the baryon charge. The properties of the model are finally compared with its baby version in (2+1) dimensions, and with the original BPS Skyrme model, contributing to a better understanding of the latter.

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arXiv2012

The gauged BPS baby Skyrme model

The baby Skyrme model is a well-known nonlinear field theory supporting topological solitons in two space dimensions. In the limit where the term quadratic in derivatives (the "sigma model term") vanishes some additional structure emerges. The resulting ("extreme" or "restricted" or "BPS") baby Skyrme model has exact soliton solutions saturating a BPS bound which exists for this restricted model. Further, the restricted model has infinitely many symmetries and infinitely many conservation laws. Here we consider the gauged version of the restricted baby Skyrme model with gauge group U(1) and the usual Maxwell term for the gauge field. We find that, again, there exists a BPS bound and BPS solutions saturating this bound. We further find that the whole problem is essentially determined by a new kind of superpotential equation. The BPS bound and the corresponding BPS solitons only may exist for potentials such that the superpotential equation has a solution which exists globally, i.e., on the whole target space. We also calculate soliton solutions both exactly and numerically, completely confirming our qualitative analytical results.

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arXiv2012

The vector BPS baby Skyrme model

We investigate the relation between the BPS baby Skyrme model and its vector meson formulation, where the baby Skyrme term is replaced by a coupling between the topological current $B_μ$ and the vector meson field $ω_μ$. The vector model still possesses infinitely many symmetries leading to infinitely many conserved currents which stand behind its solvability. It turns out that the similarities and differences of the two models depend strongly on the specific form of the potential. We find, for instance, that compactons (which exist in the BPS baby Skyrme model) disappear from the spectrum of solutions of the vector counterpart. Specifically, for the vector model with the old baby Skyrme potential we find that it has compacton solutions only provided that a delta function source term effectively screening the topological charge is inserted at the compacton boundary. For the old baby Skyrme potential squared we find that the vector model supports exponentially localized solitons, like the BPS baby Skyrme model. These solitons, however, saturate a BPS bound which is a nonlinear function of the topological charge and, as a consequence, higher solitons are unstable w.r.t. decay into smaller ones, which is at variance with the more conventional situation (a linear BPS bound and stable solitons) in the BPS baby Skyrme model.

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