Geometric Transitions, del Pezzo Surfaces and Open String Instantons

Diaconescu, Duiliu-Emanuel; Florea, Bogdan; Grassi, Antonella

Geometric Transitions, del Pezzo Surfaces and Open String Instantons

Authors

Diaconescu, Duiliu-Emanuel

Florea, Bogdan

Grassi, Antonella

Description

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.
62 pages, 3 figures, published version