论文标题
从多盖孔到黑洞：复杂马鞍的作用
From multi-gravitons to Black holes: The role of complex saddles
论文作者
论文摘要
通过在双维积分上应用Atiyah-Bott-Berline-vergne eprivarne集成公式，我们找到了一种计算矩阵积分表示$ 4D $ $ \ MATHCAL {n} = 1 $ superConformal Indices的方法。最终公式使我们能够轻松地在某些理论的大量扩展中提取分析结果。例如，我们将领先的一环校正计算为这些理论中已知的复杂马鞍的有效作用。对于$ su（n）$ $ \ MATHCAL {n} = 4 $ SYM的超符号索引，我们使用Equivariant Integration公式和Picard-Lefschetz方法表明，在$ n $中，只有两个，只有两个$ n $的价值，在已知的复杂鞍中，只有大型运营商的数量，即与订购的大型运营商的数量。出现了其他已知的复杂马鞍的贡献，但我们表明它们在这一指控中被指数抑制。电荷越小，最终对小型操作员（即电荷小于$ n^{2/3} $的运营商）进行计数越小，就像多gravitons一样，他们不能忽略它们。
By applying the Atiyah-Bott-Berline-Vergne equivariant integration formula upon double dimensional integrals, we find a way to compute the matrix integral representations of $4d$ $\mathcal{N}=1$ superconformal indices. The final formula allows us to easily extract analytic results in the large-rank expansion of certain theories. As an example, we compute the leading one-loop corrections to the effective action of the known complex saddles in those theories. For a superconformal index of $SU(N)$ $\mathcal{N}=4$ SYM, we use the equivariant integration formula and the Picard-Lefschetz method to show that at large enough values of $N$, only two, among the known complex saddles, dominate the counting of large operators i.e. of operators with charges of order $N^2$. Contributions from other known complex saddles are present, but we show they are exponentially suppressed in that range of charges; the smaller the charges the less suppressed they are, and eventually, to count small operators i.e. operators with charges smaller than $N^{2/3}$, like multi-gravitons, they can not be neglected.
