Sublattice counting and orbifolds
Sublattice counting and orbifolds
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亚晶格计数和轨道折叠
DOI：
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发表时间：
2010
期刊：
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通讯作者：
S. Reffert
中科院分区：
文献类型：
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作者：
A. Hanany;D. Orlando;S. Reffert
已知$ \mathbb{C}^{3} $的阿贝尔轨道是由六边形膜平铺编码的。到目前为止，还不知道如何计算所有这样的轨道。我们利用晶体学中的数论技术和波利亚枚举定理来填补这一空白。结果用配分函数和狄利克雷级数进行了漂亮的编码。同样的方法也适用于计算任意环状非紧化Calabi-Yau奇点的轨道。作为额外的例子，我们计算了confold、Laba理论和$ \mathbb{C}^{4} $的轨道。
Abelian orbifolds of $ \mathbb{C}^{3} $ are known to be encoded by hexagonal brane tilings. To date it is not known how to count all such orbifolds. We fill this gap by employing number theoretic techniques from crystallography, and by making use of Polya's Enumeration Theorem. The results turn out to be beautifully encoded in terms of partition functions and Dirichlet series. The same methods apply to counting orbifolds of any toric non-compact Calabi-Yau singularity. As additional examples, we count the orbifolds of the conifold, of the Laba theories, and of $ \mathbb{C}^{4} $.