string theory and moonshine phenomena
| Project/Area Number |
25400273
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Rikkyo University |
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Principal Investigator |
EGUCHI Tohru 立教大学, 理学部, 特定課題研究員 (20151970)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥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)
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| 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 |
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| 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.
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Report
(6 results)
Research Products
(25 results)
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[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)
Related Report
Invited
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[Book] 共形場理論2015
Author(s)
江口 徹、 菅原 祐二
Total Pages
320
Publisher
岩波書店
Related Report
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