Large {$N$} duality for compact Calabi-Yau threefolds

We study geometric transitions for topological strings on compact Calabi-Yau hypersurfaces in toric varieties. Large {N} duality predicts an equivalence between topological open and closed string theories connected by an extremal transition. We develop new open string enumerative techniques and perform a high-precision genus zero test of this conjecture for a certain class of toric extremal transitions. Our approach is based on (a) an open string version of Gromov-Witten theory with convex obstruction bundle and (b) an extension of Chern-Simons theory treating the framing as a formal variable.

2010 Mathematics Subject Classification

Primary 14J32. Secondary 32Qxx.

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Published 1 January 2005