Investigating topology of lattice gauge theory with domain-wall fermion

• Project Area: Discrete Geometric Analysis for Materials Design
• Project/Area Number: 18H04484
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Research Institution: Osaka University
• Principal Investigator: 深谷 英則 大阪大学, 理学研究科, 助教 (70435676)
• Project Period (FY): 2018-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥6,500,000 (Direct Cost: ¥5,000,000、Indirect Cost: ¥1,500,000); Fiscal Year 2019: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000); Fiscal Year 2018: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
• Keywords: トポロジー / 指数定理 / ドメインウォールフェルミオン / 格子ゲージ理論

Outline of Annual Research Achievements

2017年、研究代表者と大野木哲也、山口哲は素粒子論でよく知られた手法を使って、Atiyah-Patodi-Singer (APS)指数定理と同じ結果を与える新しい定式化を 見出した。非局所的境界条件を必要とせず、ドメインウォールフェルミオンとして知られるトポロジ カル絶縁体のよい模型となる演算子を用い、 APS と同じ結 果を与える物理量を定式化した。この研究は数学者からも大きな反響を呼び、指数定理の専門家である古田幹雄、松尾信一郎、山下真由子が共同研究に加わり、 物理、 数学の分野をまたがる共同研究へと発展した。その結果、「任意の偶数次元多様体で与えられる APS 指数に対し、 それと同じ結果を与えるドメイン ウォール フェルミオンの演算子が存在する」ことの 数学的証明を与えることができた。具体的には一次元高い仮想的な時空を用意、そこで曲がったドメイン ウォールを考えることにより、その時空上でのDirac 演算子の指数が2通りの手法で評価できることを証明、その一方が従来のAPS指数、もう一方がドメイン ウォールフェルミオンDirac 演算子のeta 不変量になることを示した。この研究はCommunication in Mathematical Physics誌に掲載された。さらに、奇数次元のmod-two指数で も同様の定式化が可能であることを示した。こちらの論文は現在査読中である。

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Research Products

• [Int'l Joint Research] Univ. of Graz(オーストリア)
• [Int'l Joint Research] Univ. of Edinburgh(英国)
• [Journal Article] Study of the axial U(1) anomaly at high temperature with lattice chiral fermions (2021)
  • Author(s): Aoki S.、Aoki Y.、Cossu G.、Fukaya H.、Hashimoto S.、Kaneko T.、Rohrhofer C.、Suzuki K.、JLQCD collaboration
  • Journal Title: Physical Review D Volume: 103 Issue: 7 Pages: 074506-074506
  • DOI: 10.1103/physrevd.103.074506
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] The Atiyah-Patodi-Singer Index and Domain-Wall Fermion Dirac Operators (2020)
  • Author(s): H. Fukaya, M. Furuta, S. Matsuo, T. Onogi, S. Yamaguchi and M. Yamashita
  • Journal Title: Communicatios in Mathematical Physics Volume: 380 Issue: 3 Pages: 1295-1311
  • DOI: 10.1007/s00220-020-03806-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Atiyah-Patodi-Singer index on a lattice (2020)
  • Author(s): Hidenori Fukaya, Naoki Kawai, Yoshiyuki Matsuki, Makito Mori, Katsumasa Nakayama, Tetsuya Onogi, Satoshi Yamaguchi
  • Journal Title: PTEP Volume: 4 Issue: 4 Pages: 1-11
  • DOI: 10.1093/ptep/ptaa031
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Towards fully nonperturbative computations of inelastic ?N scattering cross sections from lattice QCD (2020)
  • Author(s): Fukaya Hidenori、Hashimoto Shoji、Kaneko Takashi、Ohki Hiroshi
  • Journal Title: Physical Review D Volume: 102 Issue: 11 Pages: 114516-114516
  • DOI: 10.1103/physrevd.102.114516
  • Peer Reviewed / Open Access
• [Journal Article] Thouless-Kohmoto-Nightingale-den Nijs formula for a general Hamiltonian (2020)
  • Author(s): Fukaya Hidenori、Onogi Tetsuya、Yamaguchi Satoshi、Wu Xi
  • Journal Title: Physical Review D Volume: 101 Issue: 7 Pages: 1-14
  • DOI: 10.1103/physrevd.101.074507
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] B to D^(*)\ell\nu form factors from N_f=2+1 QCD with Mobius domain-wall quarks (2019)
  • Author(s): Kaneko Takashi、Aoki Yasumichi、Colquhoun Brian、Fukaya Hidenori、Hashimoto Shoji、JLQCD Collaboration
  • Journal Title: PoS Lattice2018 Volume: 1 Pages: 1-7
  • DOI: 10.22323/1.334.0311
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Axial U(1) symmetry and Dirac spectra in high-temperature phase of $N_f=2$ lattice QCD (2019)
  • Author(s): Suzuki Kei、Aoki Sinya、Aoki Yasumichi、Cossu Guido、Fukaya Hidenori、Hashimoto Shoji、JLQCD Collaboration
  • Journal Title: PoS Lattice2018 Volume: 1 Pages: 1-7
  • DOI: 10.22323/1.334.0152
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Observation of approximate SU(2) and SU(2n) symmetries in high temperature lattice QCD (2019)
  • Author(s): Rohrhofer Christian、Aoki Yasumichi、Cossu Guido、Fukaya Hidenori、Glozman Leonid、Hashimoto Shoji、Lang Christian B.、Prelovsek Sasa
  • Journal Title: Nuclear Physics A Volume: 982 Pages: 207-210
  • DOI: 10.1016/j.nuclphysa.2018.10.037
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Symmetries of spatial meson correlators in high temperature QCD (2019)
  • Author(s): C. Rohrhofer, Y. Aoki, G. Cossu, H. Fukaya, C. Gattringer, L. Ya. Glozman, S. Hashimoto, C.B. Lang, and S. Prelovsek
  • Journal Title: Physical Review D Volume: 100 Issue: 1 Pages: 014502-014502
  • DOI: 10.1103/physrevd.100.014502
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] Axial U(1) anomaly in 2+1-flavor lattice QCD at high temperature near the physical point (2021)
  • Author(s): 深谷英則
  • Organizer: 日本物理学会第76回年次大会
• [Presentation] What is chiral susceptibility probing? (2021)
  • Author(s): Hidenori Fukaya
  • Organizer: FunQCD: from first principles to effective theories(国際学会)
  • Int'l Joint Research
• [Presentation] A new perspective to hadronic excitations above Tc (2020)
  • Author(s): Christian Rohrhofer
  • Organizer: Asia-Pacific Symposium for Lattice Field Theory (APLAT 2020)
  • Int'l Joint Research
• [Presentation] Axial U(1) anomaly in 2+1 flavor QCD at high temperature (2020)
  • Author(s): 金森逸作
  • Organizer: 日本物理学会2020年秋季大会
• [Presentation] What is chiral susceptibility probing? (2020)
  • Author(s): Hidenori Fukaya
  • Organizer: Asia-Pacific Symposium for Lattice Field Theory (APLAT 2020)(国際学会)
  • Int'l Joint Research
• [Presentation] カイラル感受率とU(1)量子異常 (2020)
  • Author(s): 深谷英則
  • Organizer: 基研研究会 素粒子物理学の進展2020
• [Presentation] Topological excitation in high temperature phase of Quantum Chromodynamics (2020)
  • Author(s): Hidenori Fukaya
  • Organizer: 筑波大学CCS International Symposium 2020
  • Int'l Joint Research
• [Presentation] 量子色力学の高温相におけるトポロジー励起 (2020)
  • Author(s): Hidenori Fukaya
  • Organizer: 第7回「京」を中核とするHPCIシステム利用研究課題 成果報告会
  • Int'l Joint Research / Invited
• [Presentation] A physicist-friendly reformulation of the Atiyah-Patodi-Singer index theorem (on a lattice) (2020)
  • Author(s): H. Fukaya
  • Organizer: 研究会「トポロジカル表面状態、ブレーンとソリトン、指数定理」
• [Presentation] Why is domain-wall fermion mathematically interesting? (2019)
  • Author(s): H. Fukaya
  • Organizer: Workshop Frontiers in Lattice QCD and related topics
  • Int'l Joint Research
• [Presentation] Domain-wall fermion and Atiyah-Patodi-Singer index (2019)
  • Author(s): H. Fukaya
  • Organizer: Lattice 2019 at Wuhan
  • Int'l Joint Research
• [Presentation] Domain-wall fermion and Atiyah-Patodi-Singer index (2019)
  • Author(s): H. Fukaya
  • Organizer: Workshop "RMT in Sub-Atomic Physics and Beyond"
  • Int'l Joint Research / Invited
• [Presentation] Mathematical proof for physicist-friendly" reformulation of Atiyah- Patodi-Singer index". (2019)
  • Author(s): H. Fukaya
  • Organizer: Workshop Strings and Fields 2019
  • Int'l Joint Research / Invited
• [Presentation] Nf=2格子QCDにおける高温領域の対称性 (2019)
  • Author(s): H. Fukaya
  • Organizer: 日本物理学会秋季大会
• [Presentation] Domain-wall fermion and Atiyah-Patodi-Singer index (2019)
  • Author(s): H. Fukaya
  • Organizer: Workshop: Mathematical approach for topological physics (II)
  • Int'l Joint Research / Invited
• [Presentation] Topology in lattice gauge theory (2019)
  • Author(s): H. Fukaya
  • Organizer: 基研研究会「場の量子論における非摂動論的手法と素粒子物理学への応用」
  • Invited
• [Presentation] AXIAL U(1) SYMMETRY IN LATTICE QCD AT HIGH TEMPERATURE (2018)
  • Author(s): H. Fukaya
  • Organizer: YKIS2018b Symposium "Recent Developments in Quark-Hadron Sciences"
  • Int'l Joint Research / Invited
• [Presentation] A physicist-friendly reformulation of the Atiyah-Patodi-Singer index theorem (2018)
  • Author(s): H. Fukaya
  • Organizer: AVENUES OF QUANTUM FIELD THEORY IN CURVED SPACETIME
  • Int'l Joint Research / Invited
• [Presentation] A physicist-friendly reformulation of the Atiyah-Patodi-Singer index theorem (2018)
  • Author(s): H. Fukaya
  • Organizer: Workshop "PROGRESS IN THE MATHEMATICS OF TOPOLOGICAL STATES OF MATTER"
  • Int'l Joint Research / Invited
• [Presentation] Axial U(1) Anomaly at High Temperature (2018)
  • Author(s): H. Fukaya
  • Organizer: Quantum Chromodynamics and Its Symmetries
  • Int'l Joint Research / Invited
• [Remarks] 深谷英則のページ 私の研究
  • URL: http://kabuto.phys.sci.osaka-u.ac.jp/~hfukaya/study.html
• [Remarks] 深谷英則のページ 私の研究
  • URL: http://www-het.phys.sci.osaka-u.ac.jp/~hfukaya/study.html