We consider a class of N=2 conformal SU(N) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the corresponding matrix model provided by localization on a sphere S4, which also encodes information on flat-space observables involving chiral operators and circular BPS Wilson loops. We review and improve known techniques for studying the matrix model in the large-N limit, deriving explicit expressions in perturbation theory for these observables. We exploit both recursive methods in the so-called full Lie algebra approach and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. The sub-class of conformal theories for which the number of fundamental hypermultiplets does not scale with N differs in the planar limit from the N=4 SYM theory only in observables involving chiral operators of odd dimension. In this case we are able to derive compact expressions which allow to push the small 't Hooft coupling expansion to very high orders. We argue that the perturbative series have a finite radius of convergence and extrapolate them numerically to intermediate couplings. This is preliminary to an analytic investigation of the strong coupling behavior, which would be very interesting given that for such theories holographic duals have been proposed.

中文翻译：

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$$ \mathcal{N} $$ = 2 个共形对称理论 $$ \mathcal{N} $$

我们考虑了一类 N=2 共形 SU(N) SYM 理论在四个维度上的基本、双指数对称和反对称表示中的物质，并研究了由球体 S4 上的定位提供的相应矩阵模型，这也对涉及手性算子和圆形 BPS 威尔逊环的平面空间可观察量的信息进行编码。我们回顾并改进了在大 N 限制中研究矩阵模型的已知技术，在微扰理论中为这些可观测值推导出显式表达式。我们利用了所谓的全李代数方法中的递归方法和基于特征值分布的更标准的 Cartan 子代数方法。基本超多重态的数量不随 N 成比例的共形理论的子类与 N=4 SYM 理论的平面极限不同，仅在涉及奇维手征算子的可观察量上。在这种情况下，我们能够推导出紧凑的表达式，允许将小的 't Hooft 耦合扩展推到非常高的阶数。我们认为微扰级数具有有限的收敛半径，并将它们数值外推到中间耦合。这是对强耦合行为的分析研究的初步研究，考虑到针对此类理论提出了全息对偶，这将非常有趣。t Hooft 耦合扩展到非常高的阶数。我们认为微扰级数具有有限的收敛半径，并将它们数值外推到中间耦合。这是对强耦合行为的分析研究的初步研究，考虑到针对此类理论提出了全息对偶，这将非常有趣。t Hooft 耦合扩展到非常高的阶数。我们认为微扰级数具有有限的收敛半径，并将它们数值外推到中间耦合。这是对强耦合行为的分析研究的初步研究，考虑到针对此类理论提出了全息对偶，这将是非常有趣的。