  We study the implication of refined topological string amplitudes in the
supersymmetric N=1 flux compactification. They generate higher derivative
couplings among the vector multiplets and graviphoton with generically
non-holomorphic moduli dependence. For a particular term, we can compute them
by assuming the geometric engineering. We claim that the Dijkgraaf-Vafa large N
matrix model with the beta-ensemble measure directly computes the higher
derivative corrections to the supersymmetric effective action of the
supersymmetric N=1$ gauge theory.
