Wave functions and Yukawa couplings in local string compactifications

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 ℙ ¹× ℙ ¹ and ℙ ². 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.