Geometric Transitions and Open String Instantons

Abstract

We investigate the physical and mathematical structure of a new class of geometric transitions proposed by Aganagic and Vafa. The distinctive aspect of these transitions is the presence of open string instanton corrections to Chern-Simons theory. We find a precise match between open and closed string topological amplitudes applying a beautiful idea proposed by Witten some time ago. The closed string amplitudes are reproduced from an open string perspective as a result of a fascinating interplay of enumerative techniques and Chern-Simons computations.

24 pages, 4 figures, published version

References in corpus (9)

• Superstrings and Topological Strings at Large N
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Counting higher genus curves in a Calabi-Yau manifold
• 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