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arXiv 2001.06645hep-th
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大R荷下的$\mathcal N=2$共形规范理论：$SU(N)$情况

$\mathcal N=2$ conformal gauge theories at large R-charge: the $SU(N)$ case

Matteo Beccaria, Francesco Galvagno, Azeem Hasan

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52 pages, 13 pdf figures. v2: expanded bibliography
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摘要：

具有整体对称性的共形理论可以在双标度区域中进行研究，在该区域中，相互作用强度减小，而整体电荷增加。在这里，我们研究一般的4d $\mathcal N=2$ $SU(N)$规范理论与共形物质含量在大R-电荷$Q_{\rm R}\to \infty$与固定的类马蹄耦合$κ= Q_{\rm R}\,g_{\rm YM}^{2}$。我们的分析涉及两类不同的自然尺度函数。第一个是建立在手征/反手征两点函数。第二个问题涉及手性算子在$\frac{1}{2}$ -BPS Wilson-Maldacena环存在下的单点函数。在秩-1 $SU(2)$的情况下，最近已被证明是由辅助手性随机矩阵模型捕获的两点扇区。我们扩展分析$SU(N)$理论，并提供了一个算法，计算任意长的扰动扩展所有考虑的模型，参数的秩。领先和次领先的贡献通过$\mathcal N=1$超空间中的三循环计算进行交叉检查。这种微扰分析确定最大的非平面费曼图作为相关的双标度极限。在Wilson-Maldacena部门，我们得到封闭的表达式的尺度函数，有效的任何秩和$κ$。作为一个应用程序，我们定量分析了大的t Hooft耦合极限$κ\gg 1$，我们确定所有的微扰和非微扰的贡献。后者与重电BPS态有关，并与它们的质谱精确对应。

英文摘要：

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 $κ= Q_{\rm R}\,g_{\rm YM}^{2}$. 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 $κ$. As an application, we analyze quantitatively the large 't Hooft coupling limit $κ\gg 1$ 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.

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