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arXiv 2007.16165hep-th
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具有稠密谱的大N超共形规范理论的分类

Classification of large N superconformal gauge theories with a dense spectrum

Prarit Agarwal, Ki-Hong Lee, Jaewon Song

备注：
59 pages, 50 figures, v2: conformal windows and references added
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摘要：

我们对四维超对称规范理论的大$N$极限进行了分类，这些理论具有流到超共形不动点的简单规范群。我们把自己限制在没有超势和有固定味道对称的那些。我们发现总共有35个类，其中8个具有手征规范不变算子的稠密谱。稠密理论的中心荷$a$和$c$在$N$中线性增长，而稀疏谱理论的中心电荷$N^2$增长相反。中心荷之间的差$a-c$可以有两个符号，并且它在稠密理论的大$N$极限中不为零。我们发现可能存在由间隙分开的多个带，或者带上方的离散谱。我们还发现了一个标准的物质含量的不动点理论，拥有一个密集或稀疏的频谱。我们发现了一些奇怪的方面，关于超对称RG流和$a$ -最大化的道路上。对于所有具有稠密谱的理论，AdS版本的弱引力猜想（包括具有多个$U(1)$的情况下的凸壳条件）对于足够大的$N$成立，即使它们不具有弱耦合引力场。

英文摘要：

We classify the large $N$ limits of four-dimensional supersymmetric gauge theories with simple gauge groups that flow to superconformal fixed points. We restrict ourselves to the ones without a superpotential and with a fixed flavor symmetry. We find 35 classes in total, with 8 having a dense spectrum of chiral gauge-invariant operators. The central charges $a$ and $c$ for the dense theories grow linearly in $N$ in contrast to the $N^2$ growth for the theories with a sparse spectrum. The difference between the central charges $a-c$ can have both signs, and it does not vanish in the large $N$ limit for the dense theories. We find that there can be multiple bands separated by a gap, or a discrete spectrum above the band. We also find a criterion on the matter content for the fixed point theory to possess either a dense or sparse spectrum. We discover a few curious aspects regarding supersymmetric RG flows and $a$-maximization along the way. For all the theories with the dense spectrum, the AdS version of the Weak Gravity Conjecture (including the convex hull condition for the cases with multiple $U(1)$'s) holds for large enough $N$ even though they do not have weakly-coupled gravity duals.

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