string theory and moonshine phenomena

2017 Fiscal Year Final Research Report

• 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
• 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