Continuous families of Z2 monopoles

Abstract

Neste trabalho estudamos monopolos Z2 em teorias de Yang?Mills?Higgs. Consideramos uma teoria com simetria su(4) espontaneamente quebrada em so(4) por um campo escalar na parte sime´trica da representac¸a~o 4 × 4. Mostramos que esta teoria apresenta monopolos Z2 e construi´mos as formas assinto´ticas destas soluc¸o~es. Estes monopolos apresentam?se em fami´lias conti´nuas de ate´ cinco para^metros, contendo a fami´lia discreta previamente conhecida. Tambe´m encontramos explicitamente as homotopias entre as soluc¸o~es as quais classificam os monopolos na classe Z2.

Abstract: In this thesis Z2 monopole solutions were studied in Yang?Mills?Higgs theories. We considered a theory with gauge symmetry su(4) being spontaneously broken to so(4) by a scalar field in the symmetric part of the 4 × 4 representation. We showed that Z2 monopoles are solutions of this theory and proceded to construct their asymptotic form. These monopoles belong to continuous families of up to five parameters containing the discrete family previously known. We also explicitly determined homotopies between solutions, thus classifying those as type Z2.