Balanced Metrics and Noncommutative Kähler Geometry
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions C∞(M) on a Kähler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kähler 2-form. We compare the geometric...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2010 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2010
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146504 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Balanced Metrics and Noncommutative Kähler Geometry / S. Lukic // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 23 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862569515923013632 |
|---|---|
| author | Lukic, S. |
| author_facet | Lukic, S. |
| citation_txt | Balanced Metrics and Noncommutative Kähler Geometry / S. Lukic // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions C∞(M) on a Kähler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kähler 2-form. We compare the geometric quantization framework with several deformation quantization approaches. We find that the balanced metrics appear naturally as a result of requiring the vacuum energy to be the constant function on the moduli space of semiclassical vacua. In the classical limit, these metrics become Kähler-Einstein (when M admits such metrics). Finally, we sketch several applications of this formalism, such as explicit constructions of special Lagrangian submanifolds in compact Calabi-Yau manifolds.
|
| first_indexed | 2025-11-26T01:42:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146504 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T01:42:57Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Lukic, S. 2019-02-09T19:31:39Z 2019-02-09T19:31:39Z 2010 Balanced Metrics and Noncommutative Kähler Geometry / S. Lukic // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 23 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14J32; 32Q15; 32Q20; 53C25; 53D50 doi:10.3842/SIGMA.2010.069 https://nasplib.isofts.kiev.ua/handle/123456789/146504 In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions C∞(M) on a Kähler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kähler 2-form. We compare the geometric quantization framework with several deformation quantization approaches. We find that the balanced metrics appear naturally as a result of requiring the vacuum energy to be the constant function on the moduli space of semiclassical vacua. In the classical limit, these metrics become Kähler-Einstein (when M admits such metrics). Finally, we sketch several applications of this formalism, such as explicit constructions of special Lagrangian submanifolds in compact Calabi-Yau manifolds. This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
 It is a pleasure to thank T. Banks, E. Diaconescu, M. Douglas, R. Karp, S. Klevtsov, and
 specially the author’s advisor G. Moore, for valuable discussions. We would like to thank as well G. Moore and G. Torroba for their comments on the manuscript, and J. Nannarone for kind encouragement and support. This work was supported by DOE grant DE-FG02-96ER40949. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Balanced Metrics and Noncommutative Kähler Geometry Article published earlier |
| spellingShingle | Balanced Metrics and Noncommutative Kähler Geometry Lukic, S. |
| title | Balanced Metrics and Noncommutative Kähler Geometry |
| title_full | Balanced Metrics and Noncommutative Kähler Geometry |
| title_fullStr | Balanced Metrics and Noncommutative Kähler Geometry |
| title_full_unstemmed | Balanced Metrics and Noncommutative Kähler Geometry |
| title_short | Balanced Metrics and Noncommutative Kähler Geometry |
| title_sort | balanced metrics and noncommutative kähler geometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146504 |
| work_keys_str_mv | AT lukics balancedmetricsandnoncommutativekahlergeometry |