2022 Fiscal Year Annual Research Report
The algebraic analysis of evanescent operators in effective field theory and their asymptotic behavior
| Project/Area Number |
22J21553
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| Allocation Type | Single-year Grants |
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| Research Institution | The University of Tokyo |
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Principal Investigator |
CAO Weiguang 東京大学, 理学系研究科, 特別研究員(DC1)
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| Project Period (FY) |
2022-04-22 – 2025-03-31
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| Keywords | renormalization / effective field theory / subsystem symmetry / noninvertible symmetry / boson-fermion duality |
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| Outline of Annual Research Achievements |
My research focused on the renormalization of effective field theory and dualities in generalized global symmetries. I published two papers and presented my findings in various conferences and workshops.
Firstly, I investigated the renormalization of scalar effective field theories. My team and I did the first calculation of anomalous dimension tensor at higher loops for scalar effective field theories. We further developed a theorem that predicts zeros in the anomalous dimension tensors. This non-linear non-renormalization theorem was proven for all quantum field theories. Our work provides a deeper understanding of effective field theories' theoretical structures and is useful for practical calculations.
Secondly, I studied lattice models with subsystem symmetry. This newly established global symmetry is attracting attention in both fields of condensed matter physics and high energy physics. I proposed a new boson-fermion duality in (2+1)d lattice models with subsystem symmetry. This duality is realized by generalized Jordan-Wigner transformation. With this duality, I found new examples of fermionic models with subsystem symmetry, which continues to deepen our understanding of this symmetry.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
I conducted research on the non-linear order of renormalization in effective field theory, and successfully proved a highly general theorem that predicts zeros in anomalous dimension tensors. This achievement fulfills my research plan on renormalization. Additionally, I conducted a study on the newly discovered subsystem symmetry and proposed new dualities, which significantly deepen our understanding of this symmetry.
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| Strategy for Future Research Activity |
For my future research, I plan to expand my findings to other theories. Specifically, I will apply the same analysis to O(N) effective field theories, which will extend the discussion of scalar effective field theories from 2 scalars to N scalars. Additionally, I aim to combine two different generalized symmetry: subsystem symmetry and noninvertible symmetry to extend the boundary of generalized global symmetry. To achieve this, I will construct additional examples to showcase the practical applications of this new symmetry.
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