The algebraic analysis of evanescent operators in effective field theory and their asymptotic behavior
| Project/Area Number |
22KJ1072
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| Project/Area Number (Other) |
22J21553 (2022)
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Multi-year Fund (2023)
Single-year Grants (2022) |
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| Section | 国内 |
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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 | 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) |
2023-03-08 – 2025-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2024: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2023: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2022: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Generalized symmetry / Conformal field theory / Effective field theory / renormalization / effective field theory / subsystem symmetry / noninvertible symmetry / boson-fermion duality |
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| Outline of Research at the Start |
Effective operators, including evanescent operators, will be studied by renormalization. Their mixing will be calculated to higher loops to extract conformal data at Wilson-fisher fixed point. New generalized symmetry will be studied, which will put constraints on low energy effective field theory.
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| Outline of Annual Research Achievements |
My research focused on studying global symmetries and their consequences in quantum field theories and lattice models. Quantum field theory describes the microscopic physics of the elementary particles (like electron and quark) and lattice models sometimes describe various exotic phases of matter either in theory or in lab. Symmetry plays a vital role in constructing the theory, imposing constraints and solving the systems. Recently, the notion of global symmetry has been generalized. I explored new generalized version of global symmetry by constructing a duality transformation in spin models in (2+1)d with subsystem symmetry which becomes a non-invertible symmetry at the self-dual point. This work opens a new direction in the exploration of generalized symmetry. Furthermore, I studied the subsystem duality transformations systematically in a bulk-boundary point view by proposing the subsystem symmetry topological field theory. I also studied the effects of evanescent operators in theories with O(N) symmetry when N is treated as a continuous variables. I found that the evanescence imposes strong constraints on the spectrum, giving infinite cases of new degeneracies when N takes integer values.
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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 have successfully construct the non-invertible symmetry in systems with subsystem symmetry by studying the subsystem Kramers-Wannier duality. This new result has extended my previous construction of subsystem Jordan-Wigner which relating boson and fermionic models with subsystem symmetry. Furthermore, I gave a systematic study of subsystem duality transformations from the bulk-boundary point of view, which generalizes the symmetry topological field theory to encompass models with subsystem symmetry. In the previous year, I have published two papers with a total 37 citations. I was invited to give seminar talks on my work in many distinguished universities and institutes.
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| Strategy for Future Research Activity |
I plan to further study new generalized symmetries and the constraints they imposes in quantum field theories and lattice models. I plan to study more duality transformations in systems with exotic symmetries, like dipole symmetry and multipole symmetry, to find more examples of non-invertible symmetry. Furthermore, I would like to search the application of the new generalized symmetry that I constructed in realistic models. Finally, I would like to study fermionic evanescent operators using the spinor representation of the O(N) group. I expect to see more new degeneracies with the help of evanescent operators.
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Report
(2 results)
Research Products
(17 results)
