Citation
Okuda, Takuya (2005) Large N dualities in topological string theory. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd05232005184326
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 Amodel on the conifold, to the Amodel on more general geometries. We also explain how the LandauGinzburg models can be used to perform the worldsheet derivation of the Bmodel large N dualities.
In the second part, we consider a class of Amodel large N dualities where the open string theory reduces through the ChernSimons theory on a lens space to a matrix model. We compute and compare the matrix model spectral curve and the CalabiYau 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 Amodel on the resolved conifold. This is a generalization of the crystal for C^3. We also consider a novel unitary matrix model for the ChernSimons theory on the threesphere and show how the crystal model for the resolved conifold is derived from the matrix model. Certain noncompact Dbranes are naturally incorporated into the crystal and the matrix model.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  ChernSimons theory; open/closed duality 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  17 May 2005 
Author Email:  takuya (AT) its.caltech.edu 
Record Number:  CaltechETD:etd05232005184326 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd05232005184326 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1977 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  24 May 2005 
Last Modified:  26 Dec 2012 02:44 
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