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The Study of Certain Evidence of Ooguri, Strominger, Vafa Conjecture for 4D Extremal Black Holes of Type and Heterotic Superstring Theories

Omidi, Farzad | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41742 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Arfaei, Hessamaddin
  7. Abstract:
  8. In 2004 Ooguri, Strominger, and Vafa could write the partition function of 4D N=2 extremal black holes in type IIA superstring theory as the square of the absolute value of the partition function of type A closed topological string theory, which had already been introduced by Edward Witten in 1990. In this study, T and S dualities were applied to the original conjecture of Ooguri, Strominger, and Vafa. By using T duality, we have verified that the conjecture holds for 4D N=2 extremal black holes of type IIB superstring theory to the one loop order in string coupling. In other words, one can write the partition function of these kinds of black holes as the square of the absolute value of the partition function of type B closed topological string theory. Furthermore, by implementing S duality, we have derived the generalized prepotential of heterotic superstring theory compactified on the manifold to one loop order in string coupling. Our results are in complete agreement with what people had previously derived in 1996. This prepotential do depend on both the Kaehler and complex structure moduli of the manifold . Therefore, the partition functions of the corresponding extremal black holes cannot be written in terms of the partition function of type A or type B topological string theories, which only depend on one kind of moduli. On the other hand, there is another kind of topological string theories named heterotic. To build this theory we merely topologically twist the left-moving or right-moving sector. We have showed that the correlation functions of this theory depends on the complex structure moduli of the target space . It seems that the correlation functions of the theory depends on the Kaehler moduli of the target space. To verify this claim needs more calculations. If this claim is true, the next step will be the computation of the total partition function of type heterotic topological string theory and its comparison to the partition function of 4D N=2 extremal black holes of heterotic superstring theory. In this manner, we can understand whether or not the OSV conjectutre holds for these types of black holes.








  9. Keywords:
  10. Topological String Theory ; Ooguri-Strodinger-Vafa Conjecture ; Extremal Black Hole ; T Duality ; S Duality ; Prepotential ; Kaeler and Complex Structure Module

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