Conformal theories with a global symmetry may be studied in the double scaling regime where the interaction strength is reduced while the global charge increases. Here, we study generic 4d $\mathcal N=2$ $SU(N)$ gauge theories with conformal matter content at large R-charge $Q_{\rm R}\to \infty$ with fixed 't Hooft-like coupling $\kappa = Q_{\rm R}\,g_{\rm YM}^{2}$. Our analysis concerns two distinct classes of natural scaling functions. The first is built in terms of chiral/anti-chiral two-point functions. The second involves one-point functions of chiral operators in presence of $\frac{1}{2}$-BPS Wilson-Maldacena loops. In the rank-1 $SU(2)$ case, the two-point sector has been recently shown to be captured by an auxiliary chiral random matrix model. We extend the analysis to $SU(N)$ theories and provide an algorithm that computes arbitrarily long perturbative expansions for all considered models, parametric in the rank. The leading and next-to-leading contributions are cross-checked by a three-loops computation in $\mathcal N=1$ superspace. This perturbative analysis identifies maximally non-planar Feynman diagrams as the relevant ones in the double scaling limit. In the Wilson-Maldacena sector, we obtain closed expressions for the scaling functions, valid for any rank and $\kappa$. As an application, we analyze quantitatively the large 't Hooft coupling limit $\kappa\gg 1$ where we identify all perturbative and non-perturbative contributions. The latter are associated with heavy electric BPS states and the precise correspondence with their mass spectrum is clarified.

中文翻译：

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N$$ \mathcal{N} $$ = 2 大 R 电荷的共形规范理论：SU(N) 情况

具有全局对称性的共形理论可以在双标度机制中研究，其中相互作用强度降低而全局电荷增加。在这里，我们研究通用 4d $\mathcal N=2$ $SU(N)$ 规范理论，在大 R-charge $Q_{\rm R}\to \infty$ 和固定的't Hooft-like 耦合下具有共形物质含量$\kappa = Q_{\rm R}\,g_{\rm YM}^{2}$。我们的分析涉及两类不同的自然缩放函数。第一个是根据手性/反手性两点函数构建的。第二个涉及存在 $\frac{1}{2}$-BPS Wilson-Maldacena 环的手性算子的单点函数。在 rank-1 $SU(2)$ 的情况下，最近显示两点扇区被辅助手征随机矩阵模型捕获。我们将分析扩展到 $SU(N)$ 理论，并提供一种算法，该算法为所有考虑的模型计算任意长的微扰扩展，在等级中是参数化的。通过 $\mathcal N=1$ 超空间中的三循环计算交叉检查领先和次要贡献。这种微扰分析将最大非平面费曼图识别为双标度限制中的相关图。在 Wilson-Maldacena 部分，我们获得了缩放函数的封闭表达式，对任何等级和 $\kappa$ 都有效。作为一个应用程序，我们定量分析了大的 't Hooft 耦合极限 $\kappa\gg 1$，其中我们识别了所有微扰和非微扰贡献。后者与重电 BPS 状态有关，并且与它们的质谱的精确对应关系得到澄清。