BPS string solutions in non-Abelian (Super) Yang-Mills theories

Full text follows: The BPS conditions for monopoles in Yang-Mills-Higgs are known for arbitrary gauge groups and are of fundamental importance. For strings solutions, the BPS conditions are quite well known only for the U(1) gauge group broken into a Z2 exact symmetry group. Our aim is to obtain these conditions for string solutions in a theory with an arbitrary gauge group broken into a non-Abelian exact symmetry group, which are the most important in nature. In order to obtain these conditions, the Higgs representations adopted are such that, for the particular case of SO(10), it produces the symmetry breaking pattern for the SO(10) GUT theory into the Standard Model. The Lagrangian used, coincides with the bosonic part of N=2 super Yang-Mills coupled to a massive hypermultiplet. (author)