Large $N$ duality for compact Calabi-Yau threefolds

Abstract

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.