  The IKKT model is proposed as a non-perturbative formulation of superstring
theory. We propose a Dirac operator on the noncommutative torus,which is
consistent with the IKKT model, based on noncommutative geometry. Next, we
consider zero-mode equations of the Dirac operator with magnetic fluxes. We
find that zero-mode solutions have the chirality and the generation structures
similar to the commutative case. Moreover, we compute Yukawa couplings of
chiral matter fields.
