Introduction to string theory: the bosonic string

In the first two chapters we outlined the general structure of the SM and of several extensions envisaged to solve or understand some of its puzzles. It is clear that the SM or any of the extensions there described are at best just the low-energy effective description of some more fundamental theory. The SMitself contains interactions which are not asymptotically free and eventually lead to ultraviolet Landau poles, and so do its GUT extensions, whose scalar sector is not asymptotically free. These issues are not resolved in the previously mentioned extensions of the SM. In particular, models with extra dimensions even worsen the ultraviolet behavior of the theories, and the partial taming of the ultraviolet by SUSY bites back when its local version drives us into (super)gravity and its non-renormalizability. Finally, the explanation of certain SM properties like the family replication and its flavour physics, as well as other SM puzzles, seem to lie at a significantly more fundamental level. Independently of the SM issues, there is the question of the quantum consistency of gravity. Einstein's gravity considered as a quantum field theory is not renormalizable, and should be regarded as an effective theory to be completed in the ultraviolet. String theory is arguably our best candidate to provide such completion and define a consistent quantum theory of gravity. String theory indeed provides an extension of Einstein's gravity, free of quantum divergences.