K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
By Miranda C. N. Cheng. 2010
150 citations recorded by the source corpus.
A close relationship between K3 surfaces and the Mathieu groups has been established in the last century. Furthermore, it has been observed recently that the elliptic genus of K3 has a natural interpretation in terms of the dimensions of representations of the largest Mathieu group M24. In this paper we first give further evidence for this possibility by studying the elliptic genus of K3 surfaces twisted by some simple symplectic automorphisms. These partition functions with insertions of elements of M24 (the McKay-Thompson series) give further information about the relevant representation. We then point out that this new "moonshine" for the largest Mathieu group is connected to an earlier observation on a moonshine of M24 through the 1/4-BPS spectrum of K3xT^2-compactified type II string theory. This insight on the symmetry of the theory sheds new light on the generalised Kac-Moody algebra structure appearing in the spectrum, and leads to predictions for new elliptic genera of K3, perturbative spectrum of the toroidally compactified heterotic string, and the index for the 1/4-BPS dyons in the d=4, N=4 string theory, twisted by elements of the group of stringy K3 isometries.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c3296a1d9678c0f63873992738c5a91e9a65fd9b
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In Geometry and Topology
- J. Duncan
- Miranda C. N. Cheng
- Tohru Eguchi
- J. Harvey
- Hirosi Ooguri
- Yuji Tachikawa
- C. Vafa
- M. Gaberdiel
In Nuclear and High Energy Physics
- Ashoke Sen
- Tohru Eguchi
- Yuji Tachikawa
- Hirosi Ooguri
- J. Duncan
- J. Harvey
- Miranda C. N. Cheng
- L. Rastelli
In Statistical and Nonlinear Physics
- Tohru Eguchi
- J. Duncan
- Yuji Tachikawa
- J. Harvey
- Hirosi Ooguri
- Ashoke Sen
- Miranda C. N. Cheng
- L. Rastelli
Citations in the corpus
- Umbral Moonshine (2012, background): “conjecture relating the H (2) g and the group G is nothing but the conjecture relating (scalarvalued) mock modular forms and the largest Mathieu group M24 that has been investigated recently [15, 19, 24, 20, 21, 22, 108, 109].”
- Notes on the K3 Surface and the Mathieu Group M 24 (2010, result): “(1)The tentative decomposition of A7 shown in the previous of this paper was not correct in view of the later study of twisted elliptic genus in [12, 13].”