D6-brane splitting on type IIA orientifolds

We study the open-string moduli of supersymmetric D6-branes, addressing both the string and field theory aspects of D6-brane splitting on type IIA orientifolds induced by open-string moduli higgsing (i.e., their obtaining VEVs). Specifically, we focus on the Z₂ × Z₂ orientifolds and address the symmetry breaking pattern for D6-branes parallel with the orientifold 6-planes as well as those positioned at angles. We demonstrate that the string theory results, i.e., D6-brane splitting and relocating in internal space, are in one to one correspondence with the field theory results associated with the higgsing of moduli in the antisymmetric representation of Sp(2N) gauge symmetry (for branes parallel with orientifold planes) or adjoint representation of U(N) (for branes at general angles). In particular, the moduli higgsing in the open-string sector results in the change of the gauge structure of D6-branes and thus changes the chiral spectrum and family number as well. As a by-product, we provide the new examples of the supersymmetric standard-like models with the electroweak sector arising from Sp(2N)_L × Sp(2N)_R gauge symmetry; and one four-family example is free of chiral Standard Model exotics.