We consider the \( \mathcal{N} \) = 2 SYM theory with gauge group SU(N) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-N ’t Hooft expansion and is dual to a particular orientifold of AdS₅ × S⁵. We analyze this gauge theory relying on the matrix model provided by localization à la Pestun. Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the ’t Hooft coupling λ. These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and also to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Padé resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk |λ| < π² of the latter.

我们考虑\( \mathcal{N} \) = 2 SYM 理论，其中规范群 SU( N ) 和物质含量由一个对称的多重态和反对称表示的一个多重态组成。这个共形理论承认一个大的N 't Hooft 展开并且对 AdS ₅ × S ⁵的特定方向折是对偶的。我们依赖于 localization à la Pestun 提供的矩阵模型来分析这个规范理论。尽管该矩阵模型具有非常重要的相互作用，但通过利用完整的李代数方法进行矩阵积分，我们表明可以根据无限矩阵以封闭形式表示一大类可观察量，这取决于 't蹄耦合λ. 这些精确的表达式可用于以非常有效的方式生成高阶微扰扩展，也可用于分析研究强耦合下的领先行为。我们成功地将这些预测与矩阵积分的直接蒙特卡罗数值评估和从非常长的微扰级数导出的 Padé 求和进行了比较，结果证明在收敛盘之外非常稳定 | λ | < π ²后者。