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arXiv 1503.07219hep-th
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c=12处的例外代数和零星群

Exceptional Algebra and Sporadic Groups at c=12

Miranda C. N. Cheng, Sarah M. Harrison, Shamit Kachru, Daniel Whalen

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37 pages, including many tables
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摘要：

在早期的工作中，我们看到，当把24个自由二维手征费米子的理论看作是${\cal N}=1$、${\cal N}=2$或${\cal N}=4$超共形场论时，它的${\mathbb Z}/2$轨道折叠允许各种零星的有限单群作为全局对称群。在这份说明中，我们表明，查看相同的理论作为一个SCFT与扩展${\cal N}=1$对称性-其中的扩展是相同的一个出现在特殊自旋$(7)$ holonomy流形上的弦紧化-产生的理论，具有全局对称性的零星群体$M_{24}, Co_2$或$Co_3$。当被这些对称性所包围的配分函数被分解为Spin（7）代数的特征标时，产生了两分量向量值模拟模形式，该模形式编码了对应于零星群的无限维模。

英文摘要：

In earlier works, it was seen that a ${\mathbb Z}/2$ orbifold of the theory of 24 free two-dimensional chiral fermions admits various sporadic finite simple groups as global symmetry groups when viewed as an ${\cal N}=1$, ${\cal N}=2$, or ${\cal N}=4$ superconformal field theory. In this note, we show that viewing the same theory as an SCFT with extended ${\cal N}=1$ symmetry -- where the extension is the same one which arises in string compactification on manifolds of exceptional Spin$(7)$ holonomy -- yields theories which have global symmetry given by the sporadic groups $M_{24}, Co_2$ or $Co_3$. The partition functions twined by these symmetries, when decomposed into characters of the Spin(7) algebra, give rise to two-component vector-valued mock modular forms encoding an infinite-dimensional module for the corresponding sporadic groups.

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