2006 Fiscal Year Final Research Report Summary
Compactification of M Theory and Manifolds with G2 Holonomy
| Project/Area Number |
15540253
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
EGUCHI Tohru The University of Tokyo, Graduate School of Science, Professor, 大学院理学系研究科, 教授 (20151970)
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| Project Period (FY) |
2003 – 2006
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| Keywords | geometrical transition / Nekrasov's formula / N=2 Liouville theory / boundary states / flux vacua / ALE space / supersonformal field theory |
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| Research Abstract |
In paper 2 we have applied the method of geometrical transition and computed the partition function of topological string theory on various non-compact Calabi-Yau manifolds using the link invariants of Chern-Simons theory. We have shown that the results of computation agree exactly with the formula proposed by Nekrasov for the N=2 supersymmetric gauge theory. And thus they establish the relation between topological string and N=2 SUSY gauge theory.
In paper 3 we have used the representation theory of N=2 supersonformal algebra and the method of modular bootstrap and derived the boundary states of N=2 Liouville theory. N=2 Liouville theory is known to be T-dual to the coset SL(2;R)/U(1) model and our results on boundary states agree well with those known in SL(2;R)/U(1) theory.
In paper 7 we have used the formula of Ashoke-Douglas for the distribution of flux vacua in type IIB string theory and evaluated the distribution function of flux vacua on the moduli space of Calabi-Yau manifolds. We have shown that the distribution function is peaked around the singular points in Calabi-Yau moduli space and have the universal behavior 1/(z^2 log z^2). Thus it diverges at the singular point z=0, however, it is still integrable around z=0 and there exist only a finite number of vacua around each Calabi-Yau singularity..
In paper 8 we have studied the geometry of non-compact Calabi-Yau manifolds like ALE spaces and have proposed formula for their. elliptic genera based on the analysis of the representation theory of N=2,4 superconformal algebras. Our formula agrees with the one suggested from the decompactification of K3 surface by means of some non-trivial theta function identity.
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