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

We examine the issue of generating the perturbatively absent ${\bf 10} \cdot {\bf 10} \cdot {{\bf 5}}^H$ 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 $ {\bf 10} \cdot {\bf 10} \cdot {\bf{\bar 5}}^H \cdot{\bf{\bar 5}}^H \cdot {\bf{\bar 5}}^H \cdot {\bf{\bar 5}}^H \cdot {\bf 1}^H \cdot {\bf 1}^H$ 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 ${\bf 10} \cdot {\bf 10} \cdot {\bf{\bar 5}}^H \cdot{\bf{\bar 5}}^H \cdot {\bf{\bar 5}}^H \cdot {\bf{\bar 5}}^H $ 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 $T^6/{\mathbb Z}_2 \times {\mathbb Z}_2'$ toroidal orientifold with torsion, whose NP contribution to the masses gets minimal as it is induced by just a duplicated disk diagram.