Large N Dualities in Topological String Theory

Citation

Okuda, Takuya (2005) Large N Dualities in Topological String Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YJVK-6M26. https://resolver.caltech.edu/CaltechETD:etd-05232005-184326

Abstract

We investigate the phenomenon of large N duality in topological string theory from three different perspectives: worldsheets, matrix models, and melting crystals.

In the first part, we utilize the technique of mirror symmetry to generalize the worldsheet derivation of the duality, originally given by Ooguri and Vafa for the A-model on the conifold, to the A-model on more general geometries. We also explain how the Landau-Ginzburg models can be used to perform the worldsheet derivation of the B-model large N dualities.

In the second part, we consider a class of A-model large N dualities where the open string theory reduces through the Chern-Simons theory on a lens space to a matrix model. We compute and compare the matrix model spectral curve and the Calabi-Yau geometry mirror to the closed string geometry, confirming the predictions of the duality.

Finally in the third part, we propose a crystal model that describes the A-model on the resolved conifold. This is a generalization of the crystal for C³. We also consider a novel unitary matrix model for the Chern-Simons theory on the three-sphere and show how the crystal model for the resolved conifold is derived from the matrix model. Certain non-compact D-branes are naturally incorporated into the crystal and the matrix model.

Thesis Files