2014 Fiscal Year Final Research Report
Integrability and symmetry in melting crystal model
| Project/Area Number |
24540223
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 近畿大学, 理工学部, 教授 (40171433)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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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 / 超対称ゲージ理論 / 超弦理論 |
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| Outline of Final Research Achievements |
Random plane partitions or melting crystal model was an old topic in the branch of combinatorics. However, it has been found surprising relations with other branches in modern mathematical physics, such as the Seiberg-Witten theory of supersymmetric gauge theories, Gromov-Witten's invariants and the mirror symmetry of Calabi-Yau 3-folds. The model has been also studied from the integrable system viewpoint. We further elucidate integrable structures of various melting crystal models, using quantum torus symmetry. It explains clearly the underlying integrable structure is Toda hierarchy and its cousins. Using the symmetry, we also derive the q-difference equations wave functions of topological branes probed in the tological vertex chains satisfy.
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| Free Research Field |
数物系科学
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