  Most intersecting D-brane vacua in the literature contain additional massless
adjoint fields in their low energy spectrum. The existence of these additional
fields make it difficult to obtain negative beta functions and, eventually,
asymptotic freedom. We address this important issue for N=1 intersecting
D-brane models, rephrasing the problems in terms of (open string) moduli
stabilization. In particular, we consider a Z2 x Z2 orientifold construction
where D6-branes wrap rigid 3-cycles and such extra adjoint fields do not arise.
We derive the model building rules and consistency conditions for intersecting
branes in this background, and provide N=1 chiral vacua free of adjoint fields.
More precisely, we construct a Pati-Salam-like model whose SU(4) gauge group is
asymptotically free. We also comment on the application of these results for
obtaining gaugino condensation in chiral D-brane models. Finally, we embed our
constructions in the framework of flux compactification, and construct new
classes of N=1 and N=0 chiral flux vacua.
