论文标题
有限的$ n $ indices和巨型Graviton扩展
Finite $N$ indices and the giant graviton expansion
论文作者
论文摘要
$ \ MATHCAL N = 4 $ SUPER-YANG MILLS理论的超符号索引具有$ u（n）$ gauge组，可以写成量规组的矩阵积分。最近，穆西（Murthy）证明，该积分可以作为对应于索引的巨型重力扩展的术语的总和，并为单个巨型重力的情况提供了明确的公式。在这里，我们给出了类似的巨型重力群岛的任意号码（$ m \ ge1 $）的明确公式。我们提供1/2和1/16 BPS索引示例，直到三个巨型重力贡献并证明矩阵积分的膨胀与超级Gravity Dual中计算的巨型重力扩展有所不同。这表明，一旦两个或多个巨型重力开始出现，巨大的重力扩展不一定是唯一的。
The superconformal index of $\mathcal N=4$ super-Yang Mills theory with $U(N)$ gauge group can be written as a matrix integral over the gauge group. Recently, Murthy demonstrated that this integral can be reexpressed as a sum of terms corresponding to a giant graviton expansion of the index, and provided an explicit formula for the case of a single giant graviton. Here we give similar explicit formulae for an arbitrary number, $m\ge1$, of giant gravitons. We provide 1/2 and 1/16 BPS index examples up to the order where three giant gravitons contribute and demonstrate that the expansion of the matrix integral differs from the giant graviton expansion computed in the supergravity dual. This shows that the giant graviton expansion is not necessarily unique once two or more giant gravitons start appearing.
