| 研究課題/領域番号 |
22KJ1072
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| 配分区分 | 基金 |
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| 研究機関 | 東京大学 |
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研究代表者 |
CAO Weiguang 東京大学, 理学系研究科, 特別研究員(DC1)
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| 研究期間 (年度) |
2023-03-08 – 2025-03-31
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| キーワード | Generalized symmetry / Conformal field theory / Effective field theory |
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| 研究実績の概要 |
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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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
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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| 今後の研究の推進方策 |
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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