Mathieu moonshine and string compactifications

• Published in: The journal of high energy physics Vol. 2013; no. 9; pp. 1 - 24
• Main Authors: Cheng, Miranda C. N., Dong, Xi, Duncan, John F. R., Harvey, Jeffrey A., Kachru, Shamit, Wrase, Timm
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 06-09-2013
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Invariants; Joining; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; Representations; String Theory; Strings; Supersymmetry; Topological Strings; Superstrings and Heterotic Strings; Conformal Field Models in String Theory; Extended Supersymmetry
• ISSN: 1029-8479
• DOI: 10.1007/JHEP09(2013)030

A
bstract
There is a ‘Mathieu moonshine’ relating the elliptic genus of
K
3 to the sporadic group
M
24
. Here, we give evidence that this moonshine extends to part of the web of dualities connecting heterotic strings compactified on
K
3 ×
T
2
to type IIA strings compactified on Calabi-Yau threefolds. We demonstrate that dimensions of
M
24
representations govern the new supersymmetric index of the heterotic compactifications, and appear in the Gromov-Witten invariants of the dual Calabi-Yau threefolds, which are elliptic fibrations over the Hirzebruch surfaces
.