2002/06/30 by Duiliu-Emanuel Diaconescu, Bogdan Florea, Antonella Grassi
Physics and Astronomy · Mathematics · #hep-th #math.AG #math.SG
published as Adv.Theor.Math.Phys. 6 (2003) 643-702 · 62 pages, 3 figures, published version
arxiv created 2003/12/27 · arxiv updated 2009/11/30
We continue the study of a class of geometric transitions proposed by Aganagic and Vafa which exhibit open string instanton corrections to Chern-Simons theory. In this paper we consider an extremal transition for a local del Pezzo model which predicts a highly nontrivial relation between topological open and closed string amplitudes. We show that the open string amplitudes can be computed exactly using a combination of enumerative techniques and Chern-Simons theory proposed by Witten some time ago. This yields a striking conjecture relating the topological amplitudes of all genus of the local del Pezzo model to a system of coupled Chern-Simons theories.