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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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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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 / 可積分性 / 量子ト－ラス / 位相的弦理論 / トポロジカルバーテックス / q-差分方程式 / q-超幾何系 / １次元戸田格子 / 同変ディラック指数 / ゲージ理論 / インスタントン / 相対論的戸田階層 / 量子多重対数関数 / 可積分構造 / 対称性 |
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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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Report
(4 results)
Research Products
(18 results)
