Confinamento de monopolo magnético em dimensões extras.

Abstract

From the electromagnetism of Maxell, Dirac [11] in 1931, mathematically, built the rst idea of magnetic monopoles, known as the Dirac Monopole. A step fur- ther in the context of such solutions was presented independently by t Hooft [53] and Polyakov [55] in 1974, showing that magnetic monopoles arose from quite gen- eral arguments, seeking the uni cation of fundamental interactions. Unlike the Dirac monopoles, Ehich are imposed solutions by hand, the monopoles in theories of Yang- Mills-Higgs appear as solutions of equations motion. These monopoles are part of a class of solutions consists of the so-called topological solutions. These solutions, monopoles of t Hooft and Polyakov, ux tubes,cosmic string, domain walls, etc., are non-trivial solutions os the equations of motion for the classical eld. These topolog- ical defects in Yang-Mills theoru has allowed the discovery of a complex structure in vacuo QCD. In QCD, the de ning characteristic of the strong interactions between quarks is that interactions becomes weak at arbitrarily short distances, a property which is usually called asymototic freedon, and extremely strong at large distance, so that the quarks are connected to each in a state of con nement. This implies that no free quarks to be found in nature. To describe the quark con nement in gauge theory SU(N), the proposal is to make an analogy with superconductivity. It is often assumed that the electric eld lines of color between a quark-antiquarki pair will be con ned in uxes. As for the con nement of quark, the Meissner e¤ect is primisinf dual mechanism to explain the con nement of magnetic monopole. In this dissertation, we seek nd a bG ( ) function, which is associated to con nement of magnetic monopole in a four-dimensional hypersuface immersed in a universe in size D=5. The rst place to look for is in non-abelian theories, such as the Georgi - Glashow model, which have magnetic monopoles as solitons solutions of the equa- tions of motion.