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Wavefunctions on magnetized branes in the conifold

We study wavefunctions on D$7$-branes with magnetic fluxes in the conifold. Since some supersymmetric embeddings of D-branes on the $AdS_5\times T^{1,1}$ geometry are known, we consider one of the embeddings, especially the spacetime filling D$7$-branes in which (a part of) the standard model is expected to be realized. The explicit form of induced metric on the D$7$-branes allows us to solve the Laplace and Dirac equations to evaluate matter wavefunctions in extra dimensions analytically. We find that the zero-mode wavefunctions can be localized depending on the configuration of magnetic fluxes on D$7$-branes, and show some phenomenological aspects.