2017 Fiscal Year Final Research Report
string theory and moonshine phenomena
Project/Area Number 
25400273

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Multiyear 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) 
20130401 – 20180331

Keywords  string theory / supersymmetry / K3 surface / moonshine phenomenon 
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.

Free Research Field 
数理物理学
