  We use the operator formalism to derive the bosonic contribution to the
twisted open string partition function in toroidal compactifications. This
amplitude describes, for instance, the planar interaction between g+1
magnetized or intersecting D-branes. We write the result both in the closed and
in the open string channel in terms of Prym differentials on the appropriate
Riemann surface. Then we focus on the g=2 case for a 2-torus. By factorizing
the twisted partition function in the open string channel we obtain an explicit
expression for the 3-twist field correlator, which is the main ingredient in
the computation of Yukawa couplings in D-brane phenomenological models. This
provides an alternative method for computing these couplings that does not rely
on the stress-energy tensor technique.
