  We compute Yukawa couplings involving chiral matter fields in toroidal
compactifications of higher dimensional super-Yang-Mills theory with magnetic
fluxes. Specifically we focus on toroidal compactifications of D=10
super-Yang-Mills theory, which may be obtained as the low-energy limit of Type
I, Type II or Heterotic strings. Chirality is obtained by turning on constant
magnetic fluxes in each of the 2-tori. Our results are general and may as well
be applied to lower D=6,8 dimensional field theories. We solve Dirac and
Laplace equations to find out the explicit form of wavefunctions in extra
dimensions. The Yukawa couplings are computed as overlap integrals of two Weyl
fermions and one complex scalar over the compact dimensions. In the case of
Type IIB (or Type I) string theories, the models are T-dual to (orientifolded)
Type IIA with D6-branes intersecting at angles. These theories may have
phenomenological relevance since particular models with SM group and three
quark-lepton generations have been recently constructed. We find that the
Yukawa couplings so obtained are described by Riemann theta-functions, which
depend on the complex structure and Wilson line backgrounds. Different patterns
of Yukawa textures are possible depending on the values of these backgrounds.
We discuss the matching of these results with the analogous computation in
models with intersecting D6-branes. Whereas in the latter case a string
computation is required, in our case only field theory is needed.
