Geometric Transitions, del Pezzo Surfaces and Open String Instantons

Details Geometric Transitions, del Pezzo Surfaces and Open String Instantons Geometric Transitions, del Pezzo Surfaces and Open String Instantons

2002-06-18

arxiv.org/abs/hep-th/0206163v6

Adv.Theor.Math.Phys. 6 (2003) 643-702

Physics

High Energy Physics

High Energy Physics - Theory

62 pages, 3 figures, published version

Scientific paper

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.

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