On the (Non) Perturbative Origin of Quark Masses in D-brane GUT Models

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We examine the issue of generating the perturbatively absent 10 · 10 · 5ʰ SU(5)/flipped SU(5)Yukawa couplings in type II D-brane orientifold compactifications of string theory both at the perturbative (PER) and the non-perturbative (NP) level. We find at the PER level, higher order terms like 10 · 10 · 5ʰ · 5ʰ · 5ʰ · 5ʰ · 1ʰ · 1ʰ in SU(5) may be responsible for the relevant quark mass generation in models with general intersecting D6-branes. Euclidean D2-brane instantons on the other hand can also generate at the NP via the term 10 · 10 · 5ʰ · 5ʰ · 5ʰ · 5ʰ the relevant quark masses by the use of just the U(1)b brane, for SU(5) and flipped SU(5) GUTS classes of models. We provide local examples of rigid O(1) instantons within the T⁶/Z₂ × Z₂' toroidal orientifold with torsion, whose NP contribution to the masses gets minimal as it is induced by just a duplicated disk diagram.