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...rtially avoided by focusing on local model building. There, the bulk geometry can be locally controlled in the limit of decoupled gravity as for example in models built in intersecting D-brane models =-=[2, 3]-=-, F-theory [4–9] or D-branes at singularities [10–14], the latter of which we focus on in this article. In such models the Standard Model matter content and couplings are completely determined by the ...

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...f the D-brane stacks and investigate the various states localized at the intersection of two stacks. Let us further specify the setup. We 4For a systemic search of realistic MSSM D-brane quivers, see =-=[38,39]-=-. For an exhaustive search of global embeddings of such quivers, see [40, 41]. – 16 – have three stacks of D6-branes wrapping three-cycles on the factorizable six-torus T 6 = T 2 × T 2 × T 2. They int...

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...tion is strongly supported by the abundance of examples in the literature in which string instantons or D-brane instantons give rise to Yukawa couplings that are forbidden in perturbation theory (see =-=[41]-=- for a comprehensive review in the context of intersecting D6-branes in type IIA orientifolds, and [42] for a discussion of D-brane instantons stretched between the visible and hidden sectors.) In F-t...

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...fication manifold, [31]. Another property 1 The generic number is three, [6, 7, 22].– 3 – relates to the novelty and richness of patterns and mechanisms for the generation of the hierarchy of masses =-=[32, 33, 34, 35, 36]-=-, a fact that is welcome in the search for realistic vacua in string theory. It is admittedly true that there are several indications favoring embedding the SM in a unified gauge group. They include t...

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...nder the D-brane gauge symmetries can be derived by multiplying the equations (3.9) and (3.2) with the three-cycles wrapped by the D6-branes and using table 4. From the tadpole constraint one obtains =-=[20, 41, 64]-=-∑ x 6=a Nx ( #( a, x) + #( a, x) ) + (Na − 4)#( a) + (Na + 4)#( a) = 0 , (3.10) which is a constraint for each D-brane stack a of the D-brane setup. Due to the absence of antisymmetric representations...

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...realizations of the SM. As we will show, the same non-perturbative instantons that contribute to these processes are also responsible for some of the forbidden Yukawa couplings in these models. As in =-=[14, 15]-=-, we can therefore trade the a priori unknown D-instanton actions against the measured Yukawa couplings, and in this way we can derive new bounds on the string mass scale from non-perturbatively gener...

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... in case a linear combination ∑ x qxU(1)x should remain massless and thus survive as abelian gauge symmetry in the low energy effective action. For a more detailed description, we refer the reader to =-=[53]-=- (for an analogous analysis see [49, 54]).10 A.1 Tadpole cancellation The tadpole cancellation condition, given by∑ x Nx ( pix + pi ′ x ) = 4piO , (A.1) is a condition on the cycles that the D-branes ...