K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
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K3 表面、N=4 Dyons 和 Mathieu 群 M24
DOI：
10.4310/cntp.2010.v4.n4.a2
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Miranda C. N. Cheng
中科院分区：
文献类型：
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作者：
Miranda C. N. Cheng
K3曲面和Mathieu群之间的密切关系是在上个世纪建立起来的。此外，最近已经观察到，K3的椭圆亏格在最大的马蒂厄群M24的表示维数方面有一个自然的解释。本文首先通过研究由简单辛自同构扭曲的K3曲面的椭圆亏格，进一步证明了这种可能性。这些插入M24元素的配分函数（McKay-Thompson级数）给出了相关表示的进一步信息。然后我们指出，最大马蒂厄群的这个新的“月光”与早先通过K3xT^2紧化的II型弦理论的1/4-BPS谱对M24的月光观测有关。这种对理论对称性的认识为出现在谱中的广义卡茨-穆迪代数结构提供了新的线索，并导致了对K3的新椭圆属、超环面紧化杂化弦的微扰谱以及d=4，N=4弦理论中1/4-BPS双子的指数的预测，这些双子被弦K3等距群的元素扭曲。
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.