Mirror Symmetries for Brane Configurations and Branes at Singularities

TL;DR

This paper explores local mirror symmetry for non-compact Calabi-Yau manifolds with brane probes, introducing generalized brane box rules that simplify gauge theory descriptions without requiring diagonal fields at intersections.

Contribution

It provides a new set of brane box rules derived from T-duality and conifold transitions, improving the understanding of gauge theories on brane probes in mirror symmetry.

Findings

Generalized brane box rules without diagonal fields

Explicit T-duality relating Calabi-Yau manifolds and their mirrors

Conifold transition interpretation of brane configurations

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 D4 resp. D5 branes, we can explicitly T-dualize three isometry directions to relate a non-compact Calabi-Yau manifold to its local mirror. The intermediate brane setup is the one that is best suited to read off the gauge theory on the probe. 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 rules as they have been discussed so far should be generalized. Our new rules do not need diagonal fields localized at the intersection. The old rules reappear on baryonic branches of the theory.