  We consider local models of magnetised D7 branes in IIB string
compactifications, focussing on cases where an explicit metric can be written
for the local 4-cycle. The presence of an explicit metric allows analytic
expressions for the gauge bundle and for the chiral matter wavefunctions
through solving the Dirac and Laplace equations. The triple overlap of the
normalised matter wavefunctions generates the physical Yukawa couplings. Our
main examples are the cases of D7 branes on P1xP1 and P2. We consider both
supersymmetric and non-supersymmetric gauge backgrounds and both Abelian and
non-Abelian gauge bundles. We briefly outline potential phenomenological
applications of our results.
