From F-theory to brane webs: Non-perturbative effects in type IIB String Theory

We analyse the flavour sector of SU(5) Grand Unified Theories in F–theory. Two classes of local models are formulated, one with enhancement to E6 where the masses of the up–type quarks are generated, and one with enhancement to either E7 or E8 where the masses for all fermions of the Standard Model are generated. A full rank 3 Yukawa matrix is attained only after the inclusion of non–perturbative effects in the compactification space. By performing a scan over the parameters defining the local models we check whether realistic masses for the fermions may be attained.

Secondly we present two example of the appearance of linear equivalence be- tween cycles in D–brane models. In the first case we show how linear equivalence is tied with kinetic mixing between open and closed string massless U(1)’s and discuss potential phenomenological implications for dark matter and unification of gauge couplings. Secondly we show how taking into account the coupling with closed string moduli some of the brane moduli may acquire a mass. We clarify the microscopic origin of this effect and its connection with linear equivalence of cycles, and finally match it with the 4d supergravity description.

Finally we discuss the application of topological string techniques for the com- putation of the Nekrasov partition function for theories in the Higgs branch. We formulate a general algorithm for the computation of the Nekrasov partition function of the 5d TN theory in a generic point of the Higgs branch. Afterwards we present a generalisation of the topological vertex applicable to a wide class of non– toric varieties. In both cases we provide some explicit examples of the application of the new rules formulated.