Final Activity Report Summary - TRAPLETTISTRINGPHENO (Unification of elementary interactions of Particle Physics via String model building: string compactification with background fluxes.) The description of the fundamental forces of nature is presently given by two phenomenological models. On one side, the electromagnetic and nuclear forces are described by the standard model of particle physics (SM). On the other side, gravity is described by general relativity, which is also the foundation stone of modern cosmology. These two models are in good agreement with experimental observations; nevertheless they are incompatible in a theoretical sense. This and other reasons suggested the existence of a more fundamental unified theory, and the best candidate we currently have is the so-called string theory. String theory states that the space and time we observe has ten dimensions, with the six additional spatial dimensions being wrapped on some internal space having very small volume. The way in which the extra dimensions are wrapped completely determines the properties of the physical laws observed from the four-dimensional perspective. Thus, we can have different phenomenological four-dimensional models depending on the properties of the internal space. The task of string phenomenology, my research field, was to obtain phenomenological models from string theory by properly wrapping the internal dimensions. In detail, the aim of my research proposal was to obtain phenomenologically appealing models with the observed chiral spectrum or with a supersymmetric version of it, the minimal supersymmetric standard model (MSSM), where all the chargeless scalar fields, also known as moduli fields, which arose generically in a string model, had a large mass. The proposed perspective in order to achieve this was to re-obtain orbifold models, where the MSSM spectrum was easily achieved, in the language of smooth Calabi-Yau compactifications, where moduli stabilisation issues could be faced in a more effective way, and finally face this last issue. The task was accomplished to a large extent. We were able to describe smooth Calabi-Yau manifolds having the orbifolds as singular limits and reproduce orbifold models having the MSSM spectrum from this perspective. With this at hand, we expected to efficiently consider the issue of moduli stabilisation in the near future, in the dual language of F-theory model building that became accessible in the last years and proved to be particularly promising. In parallel, the issue of understanding how supersymmetry (SUSY) could be broken in a string model and the phenomenological consequences this had on the models was faced. This issue was complementary to the previously described one, but was equally fundamental, since SUSY was needed as an approximate symmetry, to be broken at some intermediate scale, in order to explain the huge hierarchy between the Planck scale and the electroweak symmetry breaking scale. We considered this final issue using a bottom-up approach. We studied various possible field theoretical models which were considered in these years and examined which constraints occurred from the requirement that they could be consistently embedded in a string model.
