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We consider local models of magnetised D7 branes in IIB stringcompactifications, focussing on cases where an explicit metric can be writtenfor the local 4-cycle. The presence of an explicit metric allows analyticexpressions for the gauge bundle and for the chiral matter wavefunctionsthrough solving the Dirac and Laplace equations. The triple overlap of thenormalised matter wavefunctions generates the physical Yukawa couplings. Ourmain examples are the cases of D7 branes on P1xP1 and P2. We consider bothsupersymmetric and non-supersymmetric gauge backgrounds and both Abelian andnon-Abelian gauge bundles. We briefly outline potential phenomenologicalapplications of our results.

Wave Functions and Yukawa Couplings in Local String Compactifications