Sólitons autoduais: vórtices e skyrmions em modelos com quebra da simetria de Lorentz

Abstract

This research presents an analysis of the existence of topological solitons through the application of the Bogomol’nyi–Prasad–Sommerfield (BPS) formalism in three distinct

effective models. These models include: an Abelian Maxwell–Higgs model with a non- minimal covariant derivative that breaks Lorentz symmetry in the CPT-odd sector; a

generalized Chern–Simons baby Skyrme model; and a Maxwell–baby Skyrme model with Lorentz-violating terms in the CPT-even sector. In some of these models, adjustments to the original Lagrangian structure were necessary to ensure the proper application of the BPS formalism. The analysis of self-dual solutions in these models revealed solitons with

distinct features, including configurations resembling Abrikosov–Nielsen–Olesen vor- tices, Compacton-like structures with Gaussian decay, and others exhibiting power-law

behavior.