AI 中文总结
研究四维大 \(N\) \(\mathcal{N}=2\) 超共形场论共形流形无穷远点处哈格多恩行为，发现整体自由极限下哈格多恩温度由特定矩阵最大特征值决定，定义两类普遍性类别，还讨论了理论构造、全息含义及相关界，解释了三类普遍性情况。
AI 中文摘要
我们对具有拉格朗日描述的四维大 \(N\) \(\mathcal{N}=2\) 超共形场论的共形流形中无穷远 点处的哈格多恩行为进行了系统研究。这些理论的许多性质可以用编码其箭图形状的李代数来理解。我们发现，在整体自由极限下，哈格多恩温度由仿射或有限卡当邻接矩阵的最大特征值决定。这定义了两类理论的普遍性类别，它们具有与弦状谱相同的高能态指数增长。第一类也是最大的一类是仿射情形，对应于 \(\mathcal{N}=4\) 超杨 - 米尔斯的轨形和定向轨形投影，且都具有相同的温度。其他的则按照 ADE 分类落入普遍性类别，其温度由对偶考克斯特数设定，可通过变形仿射情形得到。我们的结果适用于所有具有任何经典规范对称性的大 \(N\) \(\mathcal{N}=2\) 箭图，包括那些具有非双基本表示带电物质的情形。我们进一步讨论了这些理论的弦理论构造及其一些全息含义，以及我们的方法如何扩展到具有较少超对称性的广泛理论家族。我们还考虑了只有部分理论变为自由的极限情况，并找到了共形场论距离猜想预测的指数率的上下界。这些界和哈格多恩温度都由相同的特征值设定，当箭图有单个规范节点时，下界饱和，这为文献中最近发现的三类普遍性情况提供了自然解释。
英文摘要
We perform a systematic survey of the Hagedorn behaviour at infinite-distance points in the conformal manifold of four-dimensional large-$N$ $\mathcal{N}=2$ Superconformal Field Theories admitting a Lagrangian description. Many properties of these theories can be understood in terms of the Lie algebra encoding the shape of their quiver. We find that in the overall-free limit, the Hagedorn temperature is determined by the largest eigenvalue of an affine or finite Cartan adjacency matrix. This defines two types of universality classes of theories sharing the same high-energy exponential growth of states characteristic of string-like spectra. The first and largest is the affine case, corresponding to orbifold and orientifold projections of $\mathcal{N}=4$ super-Yang-Mills, and all share the same temperature. The others fall into universality classes following an ADE classification with a temperature set by the dual Coxeter number, and can be obtained by deforming the affine case. Our results apply to all large-$N$ $\mathcal{N}=2$ quivers with any classical gauge symmetry, including those with matter charged beyond bifundamental representations. We further discuss the string-theoretic construction of these theories and some of the holographic implications, as well as how our methods extend to broad families of theories with less supersymmetry. We also consider limits where only part of the theory becomes free, and find lower and upper bounds on the exponential rate predicted by the CFT Distance Conjecture. Both these bounds and the Hagedorn temperature are set by the same eigenvalue, and when the quiver has a single gauge node the lower bound is saturated, giving a natural explanation for the three universality classes recently found in the literature.
Comments47 pages + appendices
