Geometric Transitions, del Pezzo Surfaces and Open String Instantons

Abstract

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

References in corpus (9)

• Superstrings and Topological Strings at Large N
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Worldsheet Derivation of a Large N Duality
• Framed knots at large N
• Mirror symmetry for open strings
• Topological closed-string interpretation of Chern-Simons theory
• Extending Mirror Conjecture to Calabi-Yau with Bundles
• Mirror Symmetry and a $G_2$ Flop
• Chern-Simons-Witten Theory as a Topological Fermi Liquid

Cited by in corpus (3)

• Tetrahedron in F-theory Compactification
• Quiver Gauge Models in F-Theory on Local Tetrahedron
• A Large N Type IIB Duality via a Spin(7) Geometric Transition as an F-theory Flop