The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi-Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite $N$ corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small size of gauge groups, and confirm that the formula correctly reproduces the finite $N$ corrections up to expected order.

中文翻译：

---

对复曲面颤动规范理论超共形指数的有限 N 修正

研究了在复曲面 Calabi-Yau 锥体中的 D3-膜上实现的颤动规范理论的超共形指数。我们使用 AdS/CFT 对应关系并研究包裹在超对称循环上的 D3-膜。我们专注于膜结构，其中单个 D3-膜被包裹在一个循环上，我们不考虑具有多个包裹的膜。我们提出了一个公式，该公式可以对由此类膜配置引起的指数进行有限的 $N$ 修正。我们将公式对几个例子的预测与规范理论方面的结果进行了比较，该结果是通过对规范群的小规模使用本地化获得的，并确认该公式正确地再现了达到预期阶数的有限 $N$ 修正。