Abstract
We study local mirror symmetry on non-compact Calabi–Yau manifolds (conifold type of singularities) in the presence of D3 brane probes. Using an intermediate brane setup of NS 5-branes `probed' by D-branes, we can explicitly T-dualize three isometry directions to relate a non-compact Calabi–Yau manifold to its local mirror. Both intervals and boxes of NS 5-branes appear as brane setups. Going from one to the other is equivalent to performing a conifold transition in the dual geometry. One result of our investigation is that the brane box constructions, as they have been discussed so far, should be modified.
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