Mirror symmetries for brane configurations and branes at singularities. (English) Zbl 0951.81053
Summary: 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.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 32J81 | Applications of compact analytic spaces to the sciences |
| 14J81 | Relationships between surfaces, higher-dimensional varieties, and physics |
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