Supersymmetric Intersecting Branes on the Type IIA T⁶/Z₄ orientifold

We study supersymmetric intersecting D6-branes wrapping 3-cycles in the Type IIA T^6/Z_4 orientifold background. As a new feature, the 3-cycles in this orbifold space arise both from the untwisted and the Z_2 twisted sectors. We present an integral basis for the homology lattice, H_3(M,Z), in terms of fractional 3-cycles, for which the intersection form involves the Cartan matrix of E8. We show that these fractional D6-branes can be used to construct supersymmetric brane configurations realizing a three generation Pati-Salam model. Via brane recombination processes preserving supersymmetry, this GUT model can be broken down to a standard-like model.