string theory and moonshine phenomena

• Project/Area Number: 25400273
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Particle/Nuclear/Cosmic ray/Astro physics
• Research Institution: Rikkyo University
• Principal Investigator: EGUCHI Tohru 立教大学, 理学部, 特定課題研究員 (20151970)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: string theory / supersymmetry / K3 surface / moonshine phenomenon / modular invariance / Mathieu group / Jacobi form / BPS state / 超弦理論 / N=4超共形不変性 / K3曲面 / BPS表現 / マシュー群 / モジュラー変換 / N=4 SCA / BPS representation / elliptic genus / moonshine phenomena / 素粒子論 / ムーンシャイン現象 / 保型形式 / superconformal algebra / moonshine

Outline of Final Research Achievements

We were concerned with the superstring theory compactified on K3 surface and expanded its elliptic genus in terms of character formulas of string theory. We are surprised to find expansion coefficients agree with the representations of the Mathieu group. This situation is analogous with the case of monstrous moonshine where Fourier expansion coefficients of modular J function agreed with the dimensions of Monster group. Thus the new phenomenon we have discovered is now called Mathieu moonshine. Mathieu moonshine is at the corner of various branches of mathematics and is also intimately related to string theory.
Mathieu moonshine contains a number of similar moonshine phenomena which are being under our extensive investigation.

Research Products

• [Journal Article] String theory and moonshine phenomenon (2017)
  • Author(s): Tohru Eguchi
  • Journal Title: The Universe Volume: 5 Pages: 16-22
  • Peer Reviewed / Open Access
• [Journal Article] Professer Nambu, string theory and the moonshine phenomenon (2016)
  • Author(s): Tohru Eguchi
  • Journal Title: Progress of Theoretical and Experimental Physics Volume: 2016 Issue: 12 Pages: 12C108-12C108
  • DOI: 10.1093/ptep/ptw132
  • Peer Reviewed / Open Access
• [Journal Article] Duality in N=4 Liouville Theory and Moonshine Phenomena (2016)
  • Author(s): Tohru Eguchi
  • Journal Title: PTEP Volume: 2016 no.6 Issue: 6 Pages: 063B02-063B02
  • DOI: 10.1093/ptep/ptw078
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Compact formulas for the completed mock modular forms (2014)
  • Author(s): T. Eguchi and Y. Sugawara
  • Journal Title: Journal of High Energy Physics Volume: 2014 Issue: 11 Pages: 1-28
  • DOI: 10.1007/jhep11(2014)156
  • Peer Reviewed / Open Access
• [Journal Article] Lattice gauge theory and the large N reduction (2014)
  • Author(s): Tohru Eguchi
  • Journal Title: Int.J.Mod.Phys.A Volume: 29 Issue: 15 Pages: 1430036-1430036
  • DOI: 10.1142/s0217751x14300361
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Enriques Moonshine (2013)
  • Author(s): Tohru Eguchi and Kazuhiro Hikami
  • Journal Title: J. Phys. A Volume: 46 Issue: 31 Pages: 312001-312001
  • DOI: 10.1088/1751-8113/46/31/312001
  • Peer Reviewed
• [Presentation] string theory and moonshine ohenomena (2016)
  • Author(s): 江口 徹
  • Organizer: NCTS (理論科学センター研究集会、台湾)
  • Place of Presentation: 国立清華大学、台湾、新竹市
  • Year and Date: 2016-12-06
  • Invited
• [Presentation] K3 surface and Moonshine Phenomenon (2016)
  • Author(s): 江口 徹
  • Organizer: 日本数学会70周年記念
  • Place of Presentation: 関西大学、大阪府、吹田市
  • Year and Date: 2016-09-15
  • Invited
• [Presentation] Moonshine Phenomena in String Theory (2016)
  • Author(s): T.Eguchi
  • Organizer: Nambu Memorial Symposium
  • Place of Presentation: Univ. of Chicago, U.S.A.
  • Year and Date: 2016-03-11
  • Int'l Joint Research / Invited
• [Presentation] Moonshine Phenomena in String Theory (2015)
  • Author(s): T.Eguchi
  • Organizer: Yoichiro Nambu's Physics
  • Place of Presentation: Osaka University (大阪府豊中市))
  • Year and Date: 2015-11-16
  • Int'l Joint Research / Invited
• [Presentation] K3 Surface and Mathieu Moonshine (2015)
  • Author(s): T.Eguchi
  • Organizer: New Moonshine, Mock Modular Form and String Theory
  • Place of Presentation: Univ. of Durham, England
  • Year and Date: 2015-08-03
  • Int'l Joint Research / Invited
• [Presentation] Quotient Singularity and Gauge Symmetry (2015)
  • Author(s): T.Eguchi
  • Organizer: 60 year anniversary of Yang-Mills Gauge Theory
  • Place of Presentation: NanYang Technological Univ., Singapore
  • Year and Date: 2015-05-25
  • Int'l Joint Research / Invited
• [Presentation] K3 surface and Mathieu moonshine (2015)
  • Author(s): Tohru Eguchi
  • Organizer: Moduli space, conformal field theory and matrix model
  • Place of Presentation: OIST, (沖縄県国頭郡)
  • Year and Date: 2015-03-16 – 2015-03-18
  • Invited
• [Presentation] K3 surface and Mathieu moonshine (2014)
  • Author(s): 江口 徹
  • Organizer: 岡潔シンポジウム
  • Place of Presentation: 奈良女子大 (奈良県奈良市)
  • Year and Date: 2014-12-07 – 2014-12-08
  • Invited
• [Presentation] Mathieu moonshine and superconformal algebra (2014)
  • Author(s): Tohru Eguchi
  • Organizer: symposium on string theory
  • Place of Presentation: Tsinghua University, Taiwan
  • Year and Date: 2014-05-15
  • Invited
• [Presentation] Puzzles and Challenges of String Theory (2014)
  • Author(s): Tohru Eguchi
  • Organizer: Colloquim of Physics Department
  • Place of Presentation: Tsinghua University, Taiwan
  • Year and Date: 2014-05-14
  • Invited
• [Presentation] Mathieu moonshine and superconformal algebra (2014)
  • Author(s): Tohru Eguchi
  • Organizer: Peter Goddard symposium
  • Place of Presentation: 東京大学、KALVI IPMU (千葉県、柏市)
  • Invited
• [Presentation] マシュームーンシャインと超共形代数 (2014)
  • Author(s): 江口 徹
  • Organizer: Superstring theory and VOA
  • Place of Presentation: 立教大学 (東京都豊島区)
  • Invited
• [Presentation] Mathieu moonshine and superconformal algebra (2014)
  • Author(s): Tohru Eguchi
  • Organizer: Arithmetic and Algebraic Geometry 2014
  • Place of Presentation: 東東京大学大学院数理科学研究科(東京都目黒区)
  • Invited
• [Presentation] 超弦理論のゆくえ (2013)
  • Author(s): 江口 徹
  • Organizer: 基礎物理学研究所創立６０周年記念シンポジウム
  • Place of Presentation: 京都大学基礎物理学研究所(京都府京都市)
  • Invited
• [Presentation] Mathieu moonshine and K3 surface (2013)
  • Author(s): Tohru Eguchi
  • Organizer: Mock modular forms, Moonshine, and String theory
  • Place of Presentation: Simons center for Geometry and Physics(NY,USA)
  • Invited
• [Book] 共形場理論 (2015)
  • Author(s): 江口 徹、 菅原 祐二
  • Total Pages: 320
  • Publisher: 岩波書店
• [Remarks]
  • URL: https://sites.google.com/rikkyo.ac.jp/mathphys/
• [Funded Workshop] Frontiers in Mathematical Physics (2017)
  • Place of Presentation: 立教大学、東京都、豊島区
  • Year and Date: 2017-01-07
• [Funded Workshop] Rikkyo MathPhys 2016 (2016)
  • Place of Presentation: Rikkyo University (東京都、豊島区)
  • Year and Date: 2016-01-09