Citation
Yang, Jie (2008) Holomorphic anomaly equations in topological string theory. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd05302008111309
Abstract
In this thesis we discuss various aspects of topological string theories. In particular we provide a derivation of the holomorphic anomaly equation for open strings and study aspects of the Ooguri, Strominger, and Vafa conjecture. Topological string theory is a computable theory. The amplitudes of the closed topological string satisfy a holomorphic anomaly equation, which is a recursive differential equation. Recently this equation has been extended to the open topological string. We discuss the derivation of this open holomorphic anomaly equation. We find that open topological string amplitudes have new anomalies that spoil the recursive structure of the equation and introduce dependence on wrong moduli (such as complex structure moduli in the Amodel), unless the disk onepoint functions vanish. We also show that a general solution to the extended holomorphic anomaly equation for the open topological string on Dbranes in a CalabiYau manifold, is obtained from the general solution to the holomorphic anomaly equations for the closed topological string on the same manifold, by shifting the closed string moduli by amounts proportional to the 't Hooft coupling. An important application of closed topological string theory is the Ooguri, Strominger, and Vafa conjecture, which states that a certain black hole partition function is a product of topological and antitopological string partition functions. However when the black hole has finite size, the relation becomes complicated. In a specific example, we find a new factorization rule in terms of a pair of functions which we interpret as the "nonperturbative' completion of the topological string partition functions.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  BCOV; U(1) Rsymmetry 
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:  20 May 2008 
NonCaltech Author Email:  jiey (AT) caltech.edu 
Record Number:  CaltechETD:etd05302008111309 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd05302008111309 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2315 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  02 Jun 2008 
Last Modified:  01 Aug 2014 17:09 
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