The F-theory realization of the rank-1 Minahan Nemeschansky (MN) E 6 , E 7 and E 8 theories leads to a description of the BPS states on the Coulomb branch in terms of Type IIB ( p, q )-string networks. Subject to a simple ansatz for the types of networks which can occur, we study the representations of the flavor symmetry group which occur in the BPS spectrum. The results we find for the E 6 and E 7 theories are in perfect agreement with previous calculations by other methods (in particular, we find that arbitrarily large representations occur), but our scheme is easier to implement and more computationally efficient. The string network picture also gives a possible explanation of the experimental observation that in rank-1 MN theories, BPS states whose charge is n times a primitive charge occur with BPS index divisible by ( − 1) n+1 n .

中文翻译：

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关于 1 级 Minahan-Nemeschansky 理论的 BPS 谱

1 级 Minahan Nemeschansky (MN) E 6 、E 7 和 E 8 理论的 F 理论实现导致根据类型 IIB ( p, q ) 弦网络对库仑分支上的 BPS 状态进行描述。根据对可能发生的网络类型的简单分析，我们研究了 BPS 谱中出现的风味对称群的表示。我们为 E 6 和 E 7 理论找到的结果与之前通过其他方法进行的计算完全一致（特别是，我们发现出现了任意大的表示），但我们的方案更容易实现且计算效率更高。弦网络图片还对实验观察给出了可能的解释，即在 1 级 MN 理论中，BPS 状态的电荷是原始电荷的 n 倍，BPS 指数可被 (-1) n+1 n 整除。