Supersymmetric standard model, branes and Del Pezzo Surfaces

The Standard Model of particle physics is one of the most important successful results of the work of the last century physicists. In this new book, the authors present topical research in the study of new developments in the Standard Model. Topics discussed include non-equilibrium theory, fractional dynamics and the physics of the terascale sector; unexplored regions in QFT and the conceptual foundations of the Standard Model; supersymmetric Standard Model, Branes and Del Pezzo surfaces; fermion condensate as Higgs substitute and Lepton flavor violation shedding light on CP-violation. Even though the Standard Model of particles has been confirme by several experiments, many questions require improvements. Beyond the problem of Grand Unification the mass gap problem, the question of hierarchies, low boson masses and dynamical soft supersymmetry breaking, there is the really hard difficult in including gravity in a full quantum paradigm of the Standard Model. The most famous scheme elaborated in order to solve the last and, possibly, all this points is String Theory. Dualities, mirror symmetry, M-theory and AdS/CFT are some of the powerful tools which permit to perform several progresses in all the mentioned directions, at least in principle. However, interactions of String Theory with phenomenology are really recent results. A way to get a contact between theory and phenomenology is the so called bottom-up approach. We will present here a possible String Theory approach to the (Minimal Supersymmetric) Standard Model based on the geometric engineering construction firs proposed in [H. Verlinde and M. Wijnholt, JHEP 0701, 106]. We will study the relevant geometry along the lines of [S.L. Cacciatori and M. Compagnoni, JHEP 1005:078,2010], and the related physics. We will study the singular orbifold C3/27, with 27 a suitable non abelian group, its geometry and show how it can be desingularized. To render technical computations as simple as possible we will work also with a simplifie toric version, studing its main properties at K-theory level, and we will discuss how such calculations should be extended to the non abelian case. The associated relevant physics will be discussed.