| Project/Area Number |
10640253
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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 |
素粒子・核・宇宙線
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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) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Superstring theory / σ model / Calabi-Yau string theory / modular invariance / A-D-E classification / topological string theory / instanton / virasoro algebra / ブラックホール |
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| Research Abstract |
In 1997 Eguchi, together with Hori and Xiong studied the topological string theory on a target space M and obtained an infinite sequence of differential operators which form a Viarsoro algebra with a central charge c = X(M) (X(M) denotes the Euler number of M). In 1998 Eguchi, together with Jinzenji and Xiong studied the free field realization of Virasoro operators and have shown that there exist a bosonic (fermionic) free field in 1+1 dimension for each even (odd) cohomology class of M. Eguchi together with Xiong further derived topological recursion relations valid in any genus using the result of 2-dimensional gravity and verified that the Viraosoro operators predict the correct nunber of holomorphic curves also in genus 2, 3. These results are now called Virasoro conjecture of quantum cohomology.
It is well-known in string theory that the geometry of Calabi-Yau manifold may be described by Landau-Ginzburg theory (CY/LG correspondence). In the gauged linear (σ model it is possible to interpole between the regime of the classical geometry of a target manifold and the regime of local geometry of extrema of some superpotential by varying its parameter. 1999 Eguchi together with Jinzenji studied CY/LG correspondence and have shown that the correspondence holds even when M is not a Calabi-Yau manifold as far as it is a spin manifold.
When the Calabi-Yau manifold degenerates and some of its cycle vanishes, there occur non-perturbative phenomena in string theory like gauge symmetry enhancement. Thus the analysis of string theory in singular Calabi-Yau manifold is of particular interest. Eguchi together with Sugawara studied the string propagation on singular Calabi-Yau manifolds and explicitly constructed modular invariant partition functions. Modular invariants are classified according the A-D-E pattern of isolated sigularities.
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