Complete intersection moduli spaces in $ mathcal{N} = 4 $ gauge theories in three dimensions
Complete intersection moduli spaces in $ mathcal{N} = 4 $ gauge theories in three dimensions
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$ mathcal{N} = 4 $ 三维规范理论中的完整交集模空间
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发表时间：
2011
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通讯作者：
Noppadol Mekareeya
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文献类型：
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作者：
A. Hanany;Noppadol Mekareeya
本文研究了一类三维N = 4规范理论的模空间，它们与一组有序整数分拆对一一对应.人们发现这些理论可以在IIB型弦理论的膜区间上实现，因此可以用线性图来描述。已知镜像对称通过交换相应有序对中的分区来作用于这样的理论，因此镜像理论的图可以用一种简单的方式写出来。每个理论的红外库仑分支可以用镜像理论希格斯分支的超凯勒商的矩映射方程来研究。我们专注于这些奇异超凯勒空间的三个无限子类是完全的交叉。计算这些空间的希尔伯特级数是为了计算生成元和关系，结果证明它们与理论的相应划分有关。对于每一个理论，我们明确地讨论了这样一个空间的生成元和它们所满足的关系。这些关系正是相应的完备交空间的定义方程。
A bstractWe study moduli spaces of a class of three dimensional $ mathcal{N} = 4 $ gauge theories which are in one-to-one correspondence with a certain set of ordered pairs of integer partitions. It was found that these theories can be realised on brane intervals in Type IIB string theory and can therefore be described using linear quiver diagrams. Mirror symmetry was known to act on such a theory by exchanging the partitions in the corresponding ordered pair, and hence the quiver diagram of the mirror theory can be written down in a straightforward way. The infrared Coulomb branch of each theory can be studied using moment map equations for a hyperKähler quotient of the Higgs branch of the mirror theory. We focus on three infinite subclasses of these singular hyperKähler spaces which are complete intersections. The Hilbert series of these spaces are computed in order to count generators and relations, and they turn out to be related to the corresponding partitions of the theories. For each theory, we explicitly discuss the generators of such a space and relations they satisfy in detail. These relations are precisely the defining equations of the corresponding complete intersection space.