The computation of the partition functions for five-dimensional supersymmetric theories from the topological vertex

• Project/Area Number: 18K13543
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 15010:Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics
• Research Institution: Tokai University
• Principal Investigator: Hayashi Hirotaka 東海大学, 理学部, 准教授 (10780273)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 超弦理論 / 超対称ゲージ理論 / Topological vertex / 't Hooft演算子 / ヒッグス枝 / 超対称指数 / 超対称性理論 / 超対称性ゲージ理論 / 高次元超対称性理論 / グロモフ-ウィッテン不変量

Outline of Final Research Achievements

While string theory may be considered as a strong candidate for the theory of everything, it can also serve as a powerful tool to analyze physical quantities from the properties of geometries. In this project, we have studied supersymmetric gauge theories, which is a type of quantum field theories, by using branes, which exist in string theory. We realized various gauge theories on branes which were supposed to be difficult to be realized on branes, and we computed their partition functions from the geometries of the branes.

Academic Significance and Societal Importance of the Research Achievements

素粒子の標準模型はゲージ理論と呼ばれる理論によって記述されており、ゲージ理論の性質を理解することやゲージ理論を系統的に解析することは非常に重要である。その際に超弦理論は、通常の場の量子論の手法とは異なる幾何学的な解析手法を与えるため、超弦理論に存在するブレーンを用いたゲージ理論の解析は以前から行われてきた。しかし、ブレーンにより全てのゲージ理論が実現されるわけではなかった。本研究はブレーンを用いて実現できるゲージ理論の種類を大幅に拡張し、また実際にそれらの分配関数の計算を行うことで、ブレーンによるゲージ理論の解析の可能性を大きく広げる役割を果たした。

Research Products

• [Int'l Joint Research] スウォンジー大学/ダラム大学(英国)
• [Int'l Joint Research] 電子科技大学/西南交通大学/中国科学院大学カブリ理論科学研究所(中国)
• [Int'l Joint Research] 韓国高等科学院(韓国)
• [Int'l Joint Research] スウォンジー大学/ダラム大学(英国)
• [Int'l Joint Research] 四川大学/電子科技大学/西南交通大学(中国)
• [Int'l Joint Research] スウォンジー大学/ダラム大学(英国)
• [Int'l Joint Research] DESY(ドイツ)
• [Int'l Joint Research] 四川大学/電子科技大学/西南交通大学(中国)
• [Int'l Joint Research] 浦項工科大学校(韓国)
• [Int'l Joint Research] サイモンズ幾何学・物理学センター(米国)
• [Int'l Joint Research] ハーバード大学/プリンストン高等研究所/サイモンズ幾何学・物理学センター(米国)
• [Int'l Joint Research] 韓国高等科学院/浦項工科大学校(韓国)
• [Int'l Joint Research] 電子科技大学/西南交通大学(中国)
• [Int'l Joint Research] ハーバード大学/プリンストン高等研究所(米国)
• [Int'l Joint Research] 韓国高等科学院/浦項工科大学校(韓国)
• [Int'l Joint Research] 電子科技大学/西南交通大学(中国)
• [Journal Article] Exploring the orthosymplectic zoo (2022)
  • Author(s): Akhond Mohammad、Carta Federico、Dwivedi Siddharth、Hayashi Hirotaka、Kim Sung-Soo、Yagi Futoshi
  • Journal Title: Journal of High Energy Physics Volume: 05/054 Issue: 5
  • DOI: 10.1007/jhep05(2022)054
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Dualities and flavored indices of M2-brane SCFTs (2022)
  • Author(s): Hayashi Hirotaka、Nosaka Tomoki、Okazaki Tadashi
  • Journal Title: Journal of High Energy Physics Volume: 10/023 Issue: 10
  • DOI: 10.1007/jhep10(2022)023
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] ABCD of ’t Hooft operators (2021)
  • Author(s): Hayashi Hirotaka、Okuda Takuya、Yoshida Yutaka
  • Journal Title: Journal of High Energy Physics Volume: 2021 Issue: 4
  • DOI: 10.1007/jhep04(2021)241
  • Peer Reviewed / Open Access
• [Journal Article] More on topological vertex formalism for 5-brane webs with O5-plane (2021)
  • Author(s): Hayashi Hirotaka、Zhu Rui-Dong
  • Journal Title: Journal of High Energy Physics Volume: 2021 Issue: 4
  • DOI: 10.1007/jhep04(2021)292
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Factorised 3d $$ \mathcal{N} $$ = 4 orthosymplectic quivers (2021)
  • Author(s): Akhond Mohammad、Carta Federico、Dwivedi Siddharth、Hayashi Hirotaka、Kim Sung-Soo、Yagi Futoshi
  • Journal Title: Journal of High Energy Physics Volume: 2021 Issue: 5
  • DOI: 10.1007/jhep05(2021)269
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] 6d/5d exceptional gauge theories from web diagrams (2021)
  • Author(s): Hayashi Hirotaka、Kim Hee-Cheol、Ohmori Kantaro
  • Journal Title: Journal of High Energy Physics Volume: 2021 Issue: 7
  • DOI: 10.1007/jhep07(2021)128
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Five-brane webs, Higgs branches and unitary/orthosymplectic magnetic quivers (2020)
  • Author(s): Mohammad Akhond, Federico Carta, Siddharth Dwivedi, Hirotaka Hayashi, Sung-Soo Kim, Futoshi Yagi
  • Journal Title: Journal of High Energy Physics Volume: 12/164 Issue: 12
  • DOI: 10.1007/jhep12(2020)164
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Complete prepotential for 5d N = 1 superconformal field theories (2020)
  • Author(s): Hayashi Hirotaka、Kim Sung-Soo、Lee Kimyeong、Yagi Futoshi
  • Journal Title: Journal of High Energy Physics Volume: 02/074 Issue: 2
  • DOI: 10.1007/jhep02(2020)074
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] The geometry of SUSY enhancement (2020)
  • Author(s): Carta Federico、Giacomelli Simone、Hayashi Hirotaka、Savelli Raffaele
  • Journal Title: Journal of High Energy Physics Volume: 02/106 Issue: 2
  • DOI: 10.1007/jhep02(2020)106
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Rank-3 antisymmetric matter on 5-brane webs (2019)
  • Author(s): Hayashi Hirotaka、Kim Sung-Soo、Lee Kimyeong、Yagi Futoshi
  • Journal Title: Journal of High Energy Physics Volume: 05/133 Issue: 5
  • DOI: 10.1007/jhep05(2019)133
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Wall-crossing and operator ordering for ’t Hooft operators in N = 2 gauge theories (2019)
  • Author(s): Hayashi Hirotaka、Okuda Takuya、Yoshida Yutaka
  • Journal Title: Journal of High Energy Physics Volume: 11/116 Issue: 11 Pages: 116-116
  • DOI: 10.1007/jhep11(2019)116
  • NAID: 130008151541
  • Peer Reviewed / Open Access
• [Journal Article] 6d SCFTs, 5d dualities and Tao web diagrams (2019)
  • Author(s): Hayashi Hirotaka、Kim Sung-Soo、Lee Kimyeong、Yagi Futoshi
  • Journal Title: Journal of High Energy Physics Volume: 05/203 Issue: 5
  • DOI: 10.1007/jhep05(2019)203
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Dualities and 5-brane webs for 5d rank 2 SCFTs (2018)
  • Author(s): Hayashi Hirotaka、Kim Sung-Soo、Lee Kimyeong、Yagi Futoshi
  • Journal Title: Journal of High Energy Physics Volume: 16 Issue: 12
  • DOI: 10.1007/jhep12(2018)016
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] 6d SO gauge theories from trivalent gluing of web diagrams (2023)
  • Author(s): 林博貴
  • Organizer: 日本物理学会2023年春季大会
• [Presentation] On Higgsings of D-type conformal matter theories from web diagrams (2022)
  • Author(s): 林博貴
  • Organizer: 日本物理学会2022年秋季大会
• [Presentation] 6d/5d exceptional gauge theories from web diagrams (2021)
  • Author(s): Hirotaka Hayashi
  • Organizer: Strings and Fields 2021
  • Int'l Joint Research
• [Presentation] More on topological vertex formalism for 5-brane webs with O5-plane (2021)
  • Author(s): 林 博貴
  • Organizer: 日本物理学会2021年秋季大会(素核宇)
• [Presentation] Exceptional gauge theories from trivalent gluing (2021)
  • Author(s): 林 博貴
  • Organizer: 日本物理学会第76回年次大会
• [Presentation] ABCD of 't Hooft operators (2020)
  • Author(s): 林 博貴
  • Organizer: 日本物理学会2020年秋季大会(素核宇)
• [Presentation] Complete prepotentials for 5d N = 1 gauge theories (2020)
  • Author(s): Hirotaka Hayashi
  • Organizer: Branes, supergravity and string phenomenology
  • Invited
• [Presentation] The Geometry of SUSY Enhancement (2020)
  • Author(s): 林 博貴
  • Organizer: 日本物理大会第75回年次大会
• [Presentation] Wall-crossing and operator ordering for 't Hooft operators in N = 2 gauge theories (2019)
  • Author(s): Hirotaka Hayashi
  • Organizer: Strings and Fields 2019
  • Int'l Joint Research
• [Presentation] On prepotentials of 5d N = 1 gauge theories (2019)
  • Author(s): 林 博貴
  • Organizer: 日本物理学会2019年秋季大会(素核宇)
• [Presentation] Complete prepotentials for 5d N = 1 gauge theories (2019)
  • Author(s): Hirotaka Hayashi
  • Organizer: Quantum Field Theories and Strings 2019
  • Int'l Joint Research / Invited
• [Presentation] Rank-3 antisymmetric matter from 5-brane webs (2019)
  • Author(s): 林博貴
  • Organizer: 日本物理学会第74回年次大会
• [Presentation] Dualities and 5-brane webs for 5d N=1 rank 2 theories (2018)
  • Author(s): 林博貴
  • Organizer: 日本物理学会2018年秋季大会(素宇)
• [Book] Differential geometry, Calabi-Yau theory, and general relativity (担当箇所タイトル：SCFTs, holography, and topological strings, 共著者名：Hirotaka Hayashi, Patrick Jefferson, Hee-Cheol Kim, Kantaro Ohmori, Cumrun Vafa, 該当ページ：pp.105～212) (2020)
  • Author(s): Huai-Dong Cao (編), Shing-Tung Yau (編)
  • Total Pages: 346
  • Publisher: International Press of Boston, Inc.
  • ISBN: 9781571463913