Study

Publications

Scientific papers(inspire)

Presentations

Recent or upcoming presentations of my research are found here.

Kaken-hi budgets

Hidenori Fukaya's research is supported by Kaken-hi budgets. Recent achievements are summarized below. For more details, please visit here.

2022-2025 Study of the index theorems with domain-wall fermions

Kiban-Kenkyu(B) 22H01219

Research goals

The purpose of this research is to theoretically and numerically explore the geometric properties of gauge theory using domain wall fermions defined on a discretized spacetime lattice. Specifically, the research advances in the following areas: 1. Mathematical formulation of the index theorem in lattice gauge theory, and 2. The investigation of the contribution of topological excitations to the phase transition in QCD near the critical temperature.

Outline of Research Achievements

We confirmed that a fermion system with a curved domain wall embedded in a square lattice generates a gravitational field and correctly reproduces the anomaly inflow described by the index theorem. See our paper: Curved domain-wall fermion and its anomaly inflow Shoto Aoki(Osaka U), Hidenori Fukaya(Osaka U), PTEP 2023 (2023) 3, 033B05 e-Print: 2212.11583 [hep-lat]
We attempted to formulate a gravitational field in a fermion system with a curved domain wall embedded in a square lattice. In doing so, we discovered that this system provides a microscopic explanation for the phenomenon where magnetic monopoles in topological insulators acquire charge. Furthermore, we found that this is also related to the doubling problem of Weyl fermions. See our papers: Magnetic monopole becomes dyon in topological insulators Shoto Aoki, Hidenori Fukaya, Naoto Kan, Mikito Koshino, Yoshiyuki Matsuki, PhysRevB.108.155104 (2023) e-Print: 2304.13954 [hep-lat] as well as A Lattice Formulation of Weyl Fermions on a Single Curved Surface Shoto Aoki, Hidenori Fukaya, Naoto Kan, PTEP 2024 (2024) 4, 043B05 e-Print: 2304.13954 [hep-lat]

2018-2021 Investigating topology of QCD with domain-wall fermion action

Kiban-Kenkyu(B) 18H01216

Outline of Research Achievements

Simulating finite temperature lattice QCD at temperatures higher than 165MeV, we have found a strong suppression of the topological excitation or the effect of the axial U(1) anomaly. We computed the axial U(1) susceptibility as well as meson/baryon two point correlation functions and found a good consistency with the disappearance of the axial U(1) anomaly in the chiral limit. This results were published in Physical Review D and we recieved the HPCI Excellent Achievement Award in 2020. Also, we achieved a clean separation of the chiral susceptibility into the axial U(1) breaking contributions from others and found the effect of the anomaly dominates the signal by 90%.

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2018-2020 Investigating topology of lattice gauge theory with domain-wall fermion

Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area) "Discrete Geometric Analysis for Materials Design"Kobo-Kenkyu 18H04484

Outline of Research Achievements

In 2017, I, Tetsuya Onogi, and Satoshi Yamaguchi discovered a new formulation using a well-known method in particle theory that provides the same results as the Atiyah-Patodi-Singer (APS) index theorem. Without requiring non-local boundary conditions, they formulated a physical quantity yielding the same results as APS, using operators that serve as good models of topological insulators known as domain wall fermions. This research garnered significant attention from mathematicians, and experts in the index theorem: Mikio Furuta, Shinichiroh Matsuo, and Mayuko Yamashita, joined the collaborative research, leading to a cross-disciplinary collaboration between physics and mathematics. As a result, we were able to provide a mathematical proof showing that "for any APS index given on an even-dimensional manifold, there exists an operator of domain wall fermion Dirac operator that gives the same result." Specifically, by preparing a virtual spacetime of one higher dimension and considering a curved domain wall in that spacetime, they proved that the index of the Dirac operator in that spacetime could be evaluated by two different methods: one being the traditional APS index and the other being the eta invariant of the domain wall fermion Dirac operator. This research was published in the journal Communications in Mathematical Physics.

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2013-2017 Application of pion effective theory to lattice QCD for controlling the finite volume effect at 1% level

Grant-in-Aid for Young Scientists (B) 25800147

Outline of Research Achievements

The goal of this study is to control finite volume effect in lattice QCD, which is one of main systematic uncertainties. We found by controling the zero-momentum modes, that 4fm lattice size is enough to extract pion form factor with its uncertainty below 1 %. We apply this result to lattice QCD simulations and determined the pion electromagnetic radius, which agrees with the experiment. We also computed the chiral condensate by measuring the Dirac eigenvalue density compared to the Banks-Casher relation in a region we found that the finite volume effect is small using chiral perturbation theory. Our estimate for the statistical and systematic uncertainty of our result is only 1.8 %.