2022 Fiscal Year Final Research Report
Nonperturbative analysis based on quantum anomaly, resurgence theory and lattice field theory
| Project/Area Number |
19K03817
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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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| Review Section |
Basic Section 15010:Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics
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| Research Institution | Kindai University (2021-2022)
Akita University (2019-2020) |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | リサージェンス理論 / 格子場の理論 / 量子異常マッチング / リノマロン / 複素古典解 / 真空の連続性 / ZN対称性 / 不定虚部相殺構造 |
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| Outline of Final Research Achievements |
We applied resurgence theory, anomaly matching, and lattice simulation to asymptotically-free quantum field theory in order to investigate its non-perturbative properties. (1)We have shown the resurgent structure of non-SUSY QFT including 2D QFT and found out how the IR-renormalon ambiguity, who is believed to be related to confinement, is cancelled. (2)We found stabilization of the vacuum structure of ZN-twisted compactified QFT by use of 't Hooft anomaly matching. (3)We have shown the robustness of the vacuum structure of 2D ZN-twisted sigma model by lattice simulation, and found that the robustness is caused by bion and fractional-instanton configurations.
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| Free Research Field |
場の量子論，素粒子論
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| Academic Significance and Societal Importance of the Research Achievements |
場の量子論の真空構造は，素粒子とその相互作用によるこの自然界の創発を理解する上で最も重要なピースである．本研究は，比較的新しい解析手法を組み合わせることで，場の量子論の真空に関するいくつかの問題の解明に重要な貢献をした．特に，赤外リノマロン不定虚部の相殺構造の解明，相転移現象のリサージェンス理論による理解，ZN真空の安定性の示唆，という3つの結果は，今後の場の量子論研究において重要な位置を占めると考えられる．新たな数学的手法を用いた本研究は，代数解析学と理論物理学の融合分野と捉えることも可能であり，そのような新領域の創始という意味でも意義のある研究だったと言える．
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