2022 Fiscal Year Annual Research Report
アノマリーマッチングに基づくゲージ理論と相構造の非摂動的研究
| Project/Area Number |
21J20877
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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 |
陳 実 東京大学, 理学系研究科, 特別研究員(DC1)
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| Project Period (FY) |
2021-04-28 – 2024-03-31
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| Keywords | Generalized symmetry / Non-invertibility / Defect operator / Topological soliton / Color confinement / Imaginary rotation / Adiabatic continuity |
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| Outline of Annual Research Achievements |
During this fiscal year, I focused on two main research activities:
(1) With collaborators, I investigated the possibility of color confinement resulting from perturbative contributions. We explored the use of an imaginary angular velocity at a high temperature, which led to a perturbatively confined phase continuously connected to the conventional nonperturbative confined phase, as well as a perturbative deconfinement-confinement phase transition. This discovery establishes a perturbative laboratory for confinement physics where we can investigate many confinement-related phenomena perturbatively.
(2) With collaborators, I challenged the conventional understanding of the conservation law of topological solitons. While the prevailing view is that solitonic symmetry is determined by homotopy groups, we discovered a far more sophisticated algebraic structure. We found a highly unconventional selection rule for the correlation function between line and point defect operators. Solitonic symmetry accounting for this cannot be group-like but non-invertible and depends on far finer topological data than homotopy groups. Besides, its invertible part is determined by some generalized cohomology like bordism, still instead of homotopy groups. This discovery also suggests a distinguished role of solitonic symmetry in understanding Abelian non-invertible symmetry, which may open up new avenues of inquiry and deepen our understanding of generalized symmetry.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
My research progress during this fiscal year has exceeded my expectations in both research activities. In particular, I did not anticipate discovering such nontrivial and surprising results. For the first activity, we managed to solve the problem analytically, which was a great surprise, and the prediction of a deconfinement-confinement phase transition was unexpected. As for the second activity, we discovered a highly unconventional topological selection rule between line and point defects that we did not foresee. This selection rule is now known to correspond to a non-invertible categorical symmetry, which was another exciting and surprising finding.
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| Strategy for Future Research Activity |
In the future, I plan to build on my research activities from this fiscal year to further investigate exciting research directions. For my first activity, I hope to explore the relationship between confinement and chiral symmetry breaking in more detail, using the perturbative scenario we developed. This will deepen our understanding of the physics of confinement and its connections to other important phenomena. For my second activity, I plan to delve deeper into the role of solitonic symmetry in understanding general non-invertible categorical symmetry. This could open up new avenues for exploring generalized symmetry, which is an exciting and rapidly developing area of research. Overall, I believe that these research directions have great potential for yielding valuable insights and advancing our understanding of fundamental physics.
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