Minahan-Nemeschansky E6理论中的BPS态
BPS states in the Minahan-Nemeschansky E6 theory
摘要：
我们使用光谱网络的方法来计算BPS状态简并在Minahan-Nemeschansky $E_6$理论，在其库仑分支，没有打开一个质量变形。BPS多重性出现在$E_6$味对称的表示中。例如，沿着电磁荷空间中最简单的射线，我们给出了第一$14$数值简并，以及作为$E_6$表示的第一$7$简并。我们发现一个复杂的频谱，表现出指数增长的多重性作为电磁荷的函数。有一个意想不到的结果：光谱与“自旋纯度”的假设是一致的（以一种非平凡的方式），即如果在这个理论中，BPS态的电磁电荷等于$n$乘以原始电荷，那么它出现在自旋- $\frac{n}{2}$多重态中。
英文摘要：
We use the method of spectral networks to compute BPS state degeneracies in the Minahan-Nemeschansky $E_6$ theory, on its Coulomb branch, without turning on a mass deformation. The BPS multiplicities come out in representations of the $E_6$ flavor symmetry. For example, along the simplest ray in electromagnetic charge space, we give the first $14$ numerical degeneracies, and the first $7$ degeneracies as representations of $E_6$. We find a complicated spectrum, exhibiting exponential growth of multiplicities as a function of the electromagnetic charge. There is one unexpected outcome: the spectrum is consistent (in a nontrivial way) with the hypothesis of "spin purity," that if a BPS state in this theory has electromagnetic charge equal to $n$ times a primitive charge, then it appears in a spin-$\frac{n}{2}$ multiplet.
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