The fundamental chiral nature of the observed quarks and leptons and the emergence of the gauge group itself are the most puzzling aspects of the standard model. Starting from general considerations of topological properties of gauge field configurations in higher space-time dimensions, it is shown that the existence of nontrivial structures in ten dimensions would determine a class of models corresponding to a grand unified theory structure with complex fermion representations with respect to ${\mathrm{SU}\left(3\right)\mathrm{}}_C\otimes {\mathrm{SU}\left(2\right)\mathrm{}}_L\otimes {\mathrm{U}\left(1\right)\mathrm{}}_Y.$ The discussion is carried out within the framework of string theories with characteristic energy scales below the Planck mass. Avoidance of topological obstructions upon continuous deformation of field configurations leads to global chiral symmetry breaking of the underlying fundamental theory, imposes rigorous restrictions on the structure of the vacuum and space-time itself, and determines uniquely the gauge structure and matter content.

Close

PrevNext

View figure in article