2022 Fiscal Year Final Research Report
New Approach to Non-perturbative Quantum Field Theory Inspired by Gradient Flow
| Project/Area Number |
18K13546
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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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 | Institute of Physical and Chemical Research (2020-2022)
Kyoto University (2019)
Kyoto Sangyo University (2018) |
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Principal Investigator |
Kikuchi Kengo 国立研究開発法人理化学研究所, 数理創造プログラム, 基礎科学特別研究員 (20792724)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | 場の量子論 / グラディエントフロー / 超対称性 / 自発的対称性の破れ |
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| Outline of Final Research Achievements |
The gradient flow is a new procedure to suppress the divergence in gauge theory. The gradient flow equation is a kind of diffusion equation, and the correlation function of the flow field given by the solution has a good property, which is called the ultraviolet (UV) finiteness. In the gradient flow, any correlator of the flowed field is UV finite without any extra renormalization at positive flow time if the four-dimensional theory is properly renormalized. This research is the foundation of the method of quantum field theory, which focuses on the properties of the equation itself.
The results of this research can be roughly divided into two categories. One is the theoretical aspect of the gradient flow equation, especially its extension to supersymmetric theory. The other is phenomenological applications, in particular, a new method to obtain sphaleron solutions and to study the phase structure of spontaneous gauge symmetry breaking using the gradient flow method.
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| Free Research Field |
素粒子論
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| Academic Significance and Societal Importance of the Research Achievements |
本研究全体を通して明らかにされたことは、グラディエントフローの方法が、極めて限定的な系にのみ成り立つものではなく、広く様々な理論において、成り立つものであるということである。これによりSU(N)Yang-Mills理論、格子ゲージ理論での応用のみに留まらず、超対称性理論、及び現象論や自発的対称性の破れの解析などの新たな応用へとつながった。本研究におけるグラディエントフローの基礎的な解析により、その適用範囲が拡張され、より一般的に理解されたことは、今後の場の量子論の解析手法の発展において、非常に大きな学術的意義をもつ。
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