Soluções localizadas em teoria clássica de campos - Lião, Matheus Alves (2024)
This thesis deals with localized structures in Classical Field Theory, with particular emphasis in topological defects and black holes. We study solutions of nonlinear field equations in several different contexts, in which solutions that are localized in a given region of space are found. First, we shall conduct a general discussion dealing with several subjects which shall prove important for the formalism we will be dealing with, and for the appropriate understanding of our solutions. This includes a discussion about the existence and nature of topological invariants, as well as an explanation of the so called Bogomol’nyi procedure, which we shall use frequently throughout this work to find global minima of the energy. Next, we investigate scalar systems in two spacetime dimensions, where we find kinks, which connect two distinct vacua and owe their topological nontriviality to a discrete vacuum variety. We then generalize those solutions to higher dimensions, in which we shall study the results of original works developed with the introduction of impurity functions, used to break translational symmetry in the theory, thus modeling eventual inhomogeneities which may arise in realistic physical description of a system. We then turn our attention to vortices from abelian gauge theories. We shall then encounter, besides the well-known Maxwell-Higgs system, original contributions developed during this PhD. These works deal with symmetry enhancement, which has several important applications. We shall also investigate the magnetic monopoles arising in Yang-Mills-Higgs theory, which we shall extend to higher symmetries as well, thus reporting on a paper published during the PhD program. Finally, we shall discuss the STU black holes that appear in supergravity and string theory, with emphasis in modal stability investigations for nonzero spin modes. This investigation led to a paper that resulted from an international cooperation.