Analysis of supersymmetric gauge theories based on ODE/IM correspondence
| Project/Area Number |
15K05043
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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 |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
Ito Katsushi 東京工業大学, 理学院, 教授 (60221769)
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| Research Collaborator |
Satoh Yuji
Suzuki Junji
Shu Hongfei
Locke Christopher
Okubo Takafumi
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 超対称性 / 量子可積分模型 / ODE/IM対応 / 共形場理論 / 可積分性 / 可積分系 / ゲージ重力対応 |
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| Outline of Final Research Achievements |
The ODE/IM correspondence describes a non-trivial relation between ordinary differential equations and quantum integrable systems. We applied the ODE/IM correspondence to supersymmetric gauge theories in the strong coupling region and obtained the following results. (1) We studied the connection problem of the linear differential equations associated with the modified affine Toda field equations based on an affine Lie algebra and obtained the Bethe ansatz equations associated with the quantum integrable models. (2) We studied the two parameter integrable deformations of SU(3) parafermion theory and found the exact formula between the deformation parameters and the effective masses of the Homogeneous sine-Gordon model. (3) We found non-trivial relations between the quantum Seiberg-Witten curve of N=2 superconformal field theories (Argyles-Douglas theories) and the quantum integrable models.
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| Academic Significance and Societal Importance of the Research Achievements |
強結合する場の量子論は,摂動論などのこれまでの伝統的な解析方法では解析が困難である。例えば, 陽子や中性子の基本構成粒子であるクォークを単独で取り出すことができないこと(クォークの閉じ込め)の厳密な証明はない。その困難さは理論が強結合であることに起因している。本研究は, 超対称性ゲージ理論において量子可積分模型を解析する手法が強結合ゲージ理論の物理を解析する上で有効であることを示したものである。ここで用いられた方法(ODE/IM対応)は場の理論の問題のみならず、他の物理分野(PT-symmetric quantum mechanics, resurgence等)への応用が期待されている。
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Report
(5 results)
Research Products
(21 results)
