Research

• Parafermionizing the Monster with Yamato Honda and Justin Kaidi, arXiv:2605.10902, JHEP (Comment)

  At a conference in Kyoto, I was chatting with Justin and mentioned that I had recently written a paper on dualities in two-dimensional theories. He then recalled a problem related to the Monster CFT that he had wanted to work on a few years ago, and invited me to collaborate on it. The Monster group is the largest sporadic finite simple group, with order roughly $8\times 10^{53}$. The Monster CFT is a CFT on which this group acts as automorphisms. It was known that one of the $\mathbb{Z}_2$ subgroups of the Monster group is self-dual under gauging, which implies the existence of Ising-type non-invertible symmetries. More generally, it was known that for primes $p$, there are also $\mathbb{Z}_p$ subgroups that are self-dual under gauging. This suggested that many more non-invertible symmetries should exist. In this paper, we investigated this expectation. This was also my first time using Mathematica. As someone who is not exactly good with computers, I think it will still take me a little while to get used to it.

• Web of dualities on non-orientable surfaces with Keita Tsuji, arXiv:2601.09067, JHEP (Comment)

  It has long been known that when a 2D bosonic theory possesses a $\mathbb{Z}_2$ symmetry, one can define operations such as gauging and fermionization, and that these operations generate a web of dualities. A key ingredient in fermionization is the one-to-one correspondence between spin structures and quadratic refinements, together with the associated Arf invariant. It is also known that an analogous correspondence exists for pin$^-$ structures, suggesting that these constructions should admit a natural extension to non-orientable cases. About half a year ago, I discussed this idea with Y. Tachikawa, and at the time it felt somewhat premature. Revisiting the problem recently, I found that during those six months a paper had already appeared that investigated the corresponding dualities. Nevertheless, it also became clear that there remained many aspects still to be explored. Motivated by this, I started working on the problem together with K. Tsuji, a junior member of our group who has stronger expertise in conformal field theory than I do. Concretely, we identified the group structure formed by these operations, constructed the associated SymTFT, and analyzed the correspondence between sectors of the Hilbert space on $S^1$. We also included explicit examples to illustrate the general framework. Much of the work that I am less comfortable with, such as producing figures and carrying out detailed computations in concrete examples, was handled almost entirely by K. Tsuji, for which I am deeply grateful. To celebrate the submission of my first co-authored paper, we went together to enjoy a bowl of Kashiwa Jiro (ultra-traditional Japanese ramen, at least in my opinion), which tasted truly exceptional. (See also his comment.)

• Vanishing of the $H^3$ obstruction for time-reversal symmetry in (2+1)D abelian bosonic TQFTs, arXiv:2509.07368, JHEP (Comment)

  We consider a time-reversal action on anyon data. In this setting, an obstruction to defining symmetry fractionalization arises, which is known as the $H^3$ obstruction. In the abelian case, no examples in which this obstruction is nontrivial had been known; however, its triviality had not yet been proven (see comment on [1805.02738] by Y. Tachikawa). Half a year later, I revisited this problem with the thought that it might now be possible to prove such a result. After spending nearly ten hours struggling at my desk and eventually giving up, I suddenly realized—while riding my bicycle home—that there was a condition I had not yet used. With this insight, I managed to complete the proof around sunrise. Looking back, the argument involves only a simple computation. Nevertheless, I believe the result is physically important, and I have therefore written it up here.

• Generalization of anomaly formula for time reversal symmetry in (2+1)D abelian bosonic TQFTs, arXiv:2508.04990, PTEP (Comment)

  I discussed higher central charges via email with Ando, with whom I became close during my stay at YITP under the Atom-Type Researcher Program, and learned about their properties. The higher central charge is a generalization of the chiral central charge and, in the abelian case, provides an invariant that can be used to diagnose the existence of a gapped boundary. On the other hand, for (2+1)D systems with time-reversal symmetry, an anomaly formula is known that constrains the possible anomaly classification, and this formula involves the chiral central charge. Motivated by this, I explored whether, in the abelian and bosonic case, the entire formula could be extended so as to incorporate the higher central charge. Somewhat unexpectedly, this turned out to work rather well: the extension is such that setting $n=1$ reproduces the original anomaly formula. Various accompanying structures also admit natural extensions. As a result, this work can be viewed as a generalization of an important formula that incorporates an important quantity. Although the physical meaning of this extension is not yet entirely clear, I decided to write it up. Given the ambiguity of its physical interpretation, I had expected the work to face substantial scrutiny during peer review. Contrary to this expectation, it was not criticized at all; rather, it received unexpectedly strong and nontrivial praise, which was very gratifying.

• On dimensions of (2+1)D abelian bosonic topological systems on non-orientable manifolds, arXiv:2502.13532, PTEP (Comment)

  When considering a time-reversal invariant (2+1)D TQFT, it is known that a certain quantity determined by the associated modular tensor category is always a nonnegative integer, and this quantity has been interpreted as the dimension of the Hilbert space on $\mathbb{RP}^2$. However, since a mathematically rigorous construction of Reshetikhin–Turaev TQFTs in the presence of time-reversal symmetry—that is, on non-orientable manifolds—is not yet known, it had remained unclear whether this quantity is indeed always an integer. The main result of this work is an algebraic proof of this integrality in the abelian and bosonic case. Originally, Tachikawa and I had intended to extend the analysis to the fermionic case as well, but this turned out to be substantially more difficult. At that point, we decided that it would be reasonable to publish the results obtained so far. I was told that he felt that his own contribution beyond this point was not sufficient for joint authorship, and that I should therefore submit the work as a single-author paper, which is what ultimately happened. From my own perspective, given that my collaborator had been actively involved in many discussions, this outcome felt somewhat unexpected.

• Master’s thesis: Topological Quantum Field Theory with Time-Reversal Symmetry (Slides) (Japanese)

Selected talks

• Seminar at Shinshu University, Online, July 2026, “Web of dualities on non-orientable surfaces” (Slides)
• Seminar at the University of Osaka, Osaka, May 2026, “Web of dualities on non-orientable surfaces” (Slides)
• Seminar at the Mathematical Institute, University of Oxford, Oxford, April 2026, “Insights from the crosscap state toward non-orientable TQFTs” (Slides)
• Seminar at the London Institute for Mathematical Sciences, London, April 2026, “Insights from the crosscap state toward non-orientable TQFTs” (Slides) (Video)
• Interfaces & Symmetry, Kyoto, March 2026, “Insights from the crosscap state toward a rigorous formulation of non-orientable TQFTs” (Slides)
• Colloquium of Theoretical Physics at Rikkyo University, Tokyo, November 2025, “Insights from the crosscap state toward a rigorous formulation of non-orientable TQFTs” (Slides)
• CREST seminar, Online, July 2025, “On dimensions of (2+1)D abelian topological systems on non-orientable surfaces” (Slides)
• Condensed matter seminar at YITP, Kyoto, May 2025, “On dimensions of (2+1)D abelian topological systems on non-orientable surfaces”
• Seminar at Kyushu University, Fukuoka, April 2025, “On dimensions of (2+1)D abelian bosonic topological systems on unoriented manifolds”

Other talks

• RFCMP, Online, June 2026, “Introduction to SymTFT and condensation defects via $\mathbb{Z}_2$ gauge theory” (Draft) (Video) (Japanese)
• RCS seminar, Online, May 2026, “TQFT入門〜Chern–Simons理論から読み取るモジュラーテンソル圏の気持ち〜” (Slides)
• RFCMP, Online, October 2025, “Reshetikhin–Turaev TQFT with time-reversal symmetry” (Draft) (Video) (Japanese)
• TFS2025, Chiba, August 2025, “Reshetikhin–Turaev不変量の向き付け不可能多様体への拡張”
• Summer School 2025, Tokyo, August 2025, “時間反転対称な位相的場の理論におけるヒルベルト空間の次元の考察” (Slides)
• Seminar for students in the fields of theoretical physics, Online, February 2025, “On dimensions of (2+1)D abelian bosonic topological systems on unoriented manifolds”

Posters

• Strings and Fields 2026, Kyoto, August 2026, “Web of dualities on non-orientable surfaces” (Poster)
• Strings and Fields 2025, Kyoto, July 2025, “Proposal for a generalization of the anomaly formula for time-reversal symmetry in (2+1)D abelian topological systems” (Poster)
• FoPM International Symposium, Tokyo, February 2025, “On dimensions of (2+1)D abelian bosonic topological systems on unoriented manifolds”

• Outstanding Performance Award: Seminar for students in the fields of theoretical physics, Online, February 2025, “On dimensions of (2+1)D abelian bosonic topological systems on unoriented manifolds”