Vórtices em teorias k-generalizadas.

Abstract

In this work, we present new results regarding topologically non-trivial configurations arising in some generalized classical field theories. We focus on static finite-energy vortices which arise when a spontaneous symmetry breaking of U(1) local gauge invariance takes place in some Abelian-Higgs models. First, we perform a brief review regarding the usual vortices. The usual structures emerge in three diferent scenarios: the Maxwell-Higgs electrodynamics, the Chern-Simons-Higgs electrodynamics and the Maxwell-Chern-Simons-Higgs electrodynamics. In all these cases, there are BPS topological vortices: energetically stable radially symmetric configurations satisfying a set of first order equations, their energy being proportional to their topological charge. We solve the BPS equations explicity for diferent values of the vorticity n, and we comment on the main features the numerical solutions we found engender. A posteriori, we introduce a generalized model, described by an arbitrary function K (X), where X = |Dϕ|2 gives the dynamic of the complex scalar field. Specifically, we choose K (X) = X − αX2, from which we get generalized non-BPS vortices only (the resulting model does not allow for BPS ones). These vortices have no electric field (as the Maxwell-Higgs ones), but also have a non-trivial topological charge (since they are topological). We then solve the second order Euler-Lagrange equations and comment on the main features the generalized solutions we found engender. Then, we introduce a second generalized model. The new model is specifed by two dimensionless functions of the scalar field, G(|ϕ|) and w (|ϕ|). These two functions are suposed to obey a constraint relating them to the unspecifed Higgs potential, V (|ϕ|). In this case, BPS topological vortices exist, and their numerical features can be quite similar, or quite diferent, from the standard ones.vi Finally, we adapt the second generalized model to the study of twinlike theories, which are diferent theories allowing the very same field solutions and the very same energy. In this case, G(|ϕ|), w (|ϕ|) and V (|ϕ|) are suposed to obey two new constraints. Here, there are twinlike BPS topological vortices related to diferent energy densities, all of them giving the very same total energy.