2022 Fiscal Year Final Research Report
Study of Integrable Models from Gauge Theories
| Project/Area Number |
17KK0087
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| Research Category |
Fund for the Promotion of Joint International Research (Fostering Joint International Research)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Yamazaki Masahito 東京大学, カブリ数物連携宇宙研究機構, 教授 (00726599)
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| Project Period (FY) |
2018 – 2022
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| Keywords | 可積分系 / 位相的場の理論 / チャーン・サイモンズ理論 |
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| Outline of Final Research Achievements |
I collaborated with Prof. Costello at Perimeter Institute and published a paper (with more than 100 pages). (1) uncovered the origin of integrable field theories (2) re-derived many know integrable models, and discovered many new ones (3) constructed completely new class of models associated with higher genus surfaces (4) discovered new integrable structures, know as quiver Yangians, and constructed representation of the infinite-dimensional algebra from statistical-mechanical model of crystal melting.
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| Free Research Field |
high energy theory, mathematical physics
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| Academic Significance and Societal Importance of the Research Achievements |
可積分系は物理的に興味のある量を厳密に解くことができる特殊な模型であり，可積分系を超えたより一般の理論を理解する上での出発点ともなるとても貴重なクラスの理論である．可積分系については物理・数学の双方の立場から数多くの研究がなされてきたが，個別の具体例の解析にとどまっていることがほとんどであった．本研究の成果により，可積分性の根源的な起源が場の理論の立場から明らかにされ，場の理論を一つの枠組みの中で系統的に議論することが可能になった．
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