2011 Fiscal Year Final Research Report
lntegrability and geometry in random plane partitions
| Project/Area Number |
21540218
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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 |
Global analysis
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| Research Institution | Setsunan University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TAKASAKI Kanehisa 京都大学, 人間環境学研究科, 教授 (40171433)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 可積分系 / 数理物理 / ランダム平面分割 / 量子トーラス / 戸田階層 / 熱力学極限 / 超対称ゲージ理論 / 超弦理論 |
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| Research Abstract |
We study integrable systems lying with geometorical structures that appear and play important roles in the recent progress of mathematical physics, in particular, gauge theories and string theories. Exact solutions for supersymmetric gauge theories and exact amplitudes of topological strings show that random partitions and random plane partitions reflect combinatorial and geometrical structures of these theories. We investigate the integrable structure(1-Toda hierarchy and its dispertion-less limit) of random plane partitions and its thermodynamic limit by utilizing quantum torus symmetry, giving the generalized string equation in a partial form. We also derive the semiclassical generalized string equation which describes the thermodynamic limit of random partitions.
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