Advances in Theoretical and Mathematical Physics

Volume 9 (2005)

Number 1

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

Pages: 31 – 128



Duiliu-Emanuel Diaconescu

Bogdan Florea


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.

Published 1 January 2005