2006 Fiscal Year Final Research Report Summary
Geometry of Higher Dimensional Black Hole and Compact Einstein Space
| Project/Area Number |
17540262
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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 | Osaka City University |
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Principal Investigator |
YASUI Yukinori Osaka City University, Mathematics and Physics, Associate Professor, 大学院理学研究科, 准教授 (30191117)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Yoshitake Osaka City University, Mathematics and Physics, Associate Professor, 大学院理学研究科, 准教授 (20271182)
SAKAGUCHI Makoto Okayama Institute for Quantum Physics, Researcher, 研究員 (90382027)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Einstein manifold / black hole / AdS / CFT correspondence / instanton |
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| Research Abstract |
We aimed to study compact Einstein manifolds and Riemannian manifolds of special holonomy from a view point of black hole.
These geometries are physically interpreted as higher dimensional gravitational instantons, and deeply related to new geometries expected by string theory. Especially, compact Sasaki-Einstein geometry has been extensively studied in connection with AdS/CFT correspondence.
1. We have constructed a new infinite series of Einstein metrics on sphere bundles. These metrics appear as a certain limit of 5-dimensional AdS Kerr black holes. In the special case, the metric gives a homogeneous Sasaki-Einstein metric. Our construction is a higher dimensional version of the method of Page, which gave an inhomogeneous Einstein metric on the first del Pezzo surface.
2. Recently, D3 branes at the tip of toric Calabi-Yau cones have been extensively studied from a view point of AdS/CFT correspondence. It is natural to consider the deformations of cone metrics in order to explore non-conformal field theories. We have constructed an explicit non-singular complete toric Calabi-Yau metric using the local solution found by Chen, Lu and Pope. This metric gives a new supergravity solution representing D3 branes.
3. We have constructed a new infinite family of quiver gauge theories which blow down to the quiver gauge theories found by Hannany, Kazakopoulos and Wecht, recently. This family includes a quiver gauge theory for the third del Pezzo surface. We have shown, using volume minimaization, that these theories generically have irrational R-charges. The AdS/CFT correspondence implies that the dual geometries are irregular toric Sasaki-Einstein manifolds.
4. We studied stationary and axially symmetric solitonic solutions of five dimensional vacuum Einstein equations by using the inverse scattering method. From five dimensional Minkowski space-time as a seed, we reproduced a black ring solution with a rotating two sphere which was found by Mishima and Iguchi recently.
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Research Products
(15 results)
