Costruzione Consistente di Stati di Bordo e Crosscap per Teorie con Orientifold

Consistent superstring theories live in a ten dimensional space-time. To reproduce the well-known physics of four dimensional Minkowski space-time, six out of ten dimension must be compactified on an internal space, typically taken to be a Calabi-Yau manifold. Orbibold and orientifold constructions can be used to describe perturbative limits of such internal geometries. The inclusion and the proper treatment of D-branes and O-planes is fundamental as they represent non-perturbative solutions to the string effective action and are required by duality transformations. Both objects admit a description in terms of closed string states called, respectively, boundary and crosscap states. Their interplay is crucial in order to obtain a divergence-free theory. In this thesis we introduce the basic theoretical framework for orbifold and orientifold theories from the point of view of the bosonic string. Focusing on fractional D-branes, the necessary consistency conditions and computational formulae are given for boundary and crosscap states. Explicit expressions are produced for two-dimensional orbifolds, obtained quotienting the complex plane by means of a discrete group of rations. These results, properly extended to the superstring case, can be used as a starting point to construct higher-dimensional theories.