Rompimientos de simetrías inducidos por una pared de dominio 𝑺𝑶(𝟏𝟎)

Abstract

The objective of this work was to determine solutions of the domain wall type to a symmetric scalar field theory under the SO (10) group, for which the Klein Gordon system and the scalar field were considered in the attached representation of SO (10). Thus, the first thing was to represent a Lagrangian in relation to the invariant more general fourth-order scalar potential under symmetry Z2 and SO (10), after this, from the Euler-Lagrange equations the equations of motion of the components of the non-abelian scalar field, a system of five ordinary differential equations, which were numerically integrated using the Limit Value Problem (BVP) method in Matlab with bvp4c. It is concluded that it was possible to find three solutions that asymptotically induced the breakdown of the SO (10) group in SU(5), which were called symmetric, asymmetric and superasymmetric, and that exhibited different patterns of break in the center of each scenario. For the symmetric case, the symmetry SO (10) was maintained while for the asymmetric scenario SO(6) XSU(2) XU(1) was recovered and for the superasymmetric scenario SU(4) XSO(2) XU(1). Finally, it is recommended to extend the Klein Gordon system to other symmetry groups associated with large unification problems where the domain wall breaks the symmetry group to the one compatible with the Standard Model.