The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds
We show that the Reeb vector, and hence in particular the volume, of a Sasaki-Einstein metric on the base of a toric Calabi-Yau cone of complex dimension n may be computed by minimising a function Z on ℝn which depends only on the toric data that defines the singularity. In this way one can extract...
| Main Authors: | , , |
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| 格式: | Journal article |
| 語言: | English |
| 出版: |
2006
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| _version_ | 1826258882496823296 |
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| author | Martelli, D Sparks, J Yau, S |
| author_facet | Martelli, D Sparks, J Yau, S |
| author_sort | Martelli, D |
| collection | OXFORD |
| description | We show that the Reeb vector, and hence in particular the volume, of a Sasaki-Einstein metric on the base of a toric Calabi-Yau cone of complex dimension n may be computed by minimising a function Z on ℝn which depends only on the toric data that defines the singularity. In this way one can extract certain geometric information for a toric Sasaki-Einstein manifold without finding the metric explicitly. For complex dimension n = 3 the Reeb vector and the volume correspond to the R-symmetry and the a central charge of the AdS/CFT dual superconformal field theory, respectively. We therefore interpret this extremal problem as the geometric dual of a-maximisation. We illustrate our results with some examples, including the Y p,q singularities and the complex cone over the second del Pezzo surface. © Springer-Verlag 2006. |
| first_indexed | 2024-03-06T18:41:03Z |
| format | Journal article |
| id | oxford-uuid:0cde9701-6f8a-4d77-a19c-10fc44939365 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:41:03Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:0cde9701-6f8a-4d77-a19c-10fc449393652022-03-26T09:37:27ZThe geometric dual of a-maximisation for toric Sasaki-Einstein manifoldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0cde9701-6f8a-4d77-a19c-10fc44939365EnglishSymplectic Elements at Oxford2006Martelli, DSparks, JYau, SWe show that the Reeb vector, and hence in particular the volume, of a Sasaki-Einstein metric on the base of a toric Calabi-Yau cone of complex dimension n may be computed by minimising a function Z on ℝn which depends only on the toric data that defines the singularity. In this way one can extract certain geometric information for a toric Sasaki-Einstein manifold without finding the metric explicitly. For complex dimension n = 3 the Reeb vector and the volume correspond to the R-symmetry and the a central charge of the AdS/CFT dual superconformal field theory, respectively. We therefore interpret this extremal problem as the geometric dual of a-maximisation. We illustrate our results with some examples, including the Y p,q singularities and the complex cone over the second del Pezzo surface. © Springer-Verlag 2006. |
| spellingShingle | Martelli, D Sparks, J Yau, S The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds |
| title | The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds |
| title_full | The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds |
| title_fullStr | The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds |
| title_full_unstemmed | The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds |
| title_short | The geometric dual of a-maximisation for toric Sasaki-Einstein manifolds |
| title_sort | geometric dual of a maximisation for toric sasaki einstein manifolds |
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