论文标题
ABJM理论的大型$ n $分区功能
Large $N$ Partition Functions of the ABJM Theory
论文作者
论文摘要
我们研究了$ \ mathrm {u}（n）_ {k} \ times \ mathrm {u}（n）_ { - k} $ abjm理论计算由SuperSymmetry-Metrymmetrictric notization计算出的$ \ mathrm {u}（n）_ {k} \ times \ mathrm {u}（n）_ {k} \ times \ mathrm {u}（n）_ {我们猜想了一个明确的表达式，对大$ n $限制中的所有订单有效，对于$ \ mathrm {u}（1）（1）\ times \ times \ mathrm {u}（1）$不变的壁球球体的分区函数在真实质量的情况下以通风的功能在场。提出了该猜想的几项非平凡测试。此外，我们为ABJM理论的拓扑扭曲索引提供了明确的紧凑表达，该索引在$ 1/n $扩展中的所有订单上有效。我们使用这些结果来得出拓扑扭曲的索引，并在“ t Hooft限制”中获得球形分区函数，该函数对应于$ \ tt g $ type IIA字符串理论自由能为$α'$扩展中的所有订单。我们讨论了结果对全息图和广告物理$ _4 $黑洞的含义。
We study the large $N$ limit of some supersymmetric partition functions of the $\mathrm{U}(N)_{k}\times \mathrm{U}(N)_{-k}$ ABJM theory computed by supersymmetric localization. We conjecture an explicit expression, valid to all orders in the large $N$ limit, for the partition function on the $\mathrm{U}(1)\times \mathrm{U}(1)$ invariant squashed sphere in the presence of real masses in terms of an Airy function. Several non-trivial tests of this conjecture are presented. In addition, we derive an explicit compact expression for the topologically twisted index of the ABJM theory valid at fixed $k$ to all orders in the $1/N$ expansion. We use these results to derive the topologically twisted index and the sphere partition function in the 't Hooft limit which correspond to genus $\tt g$ type IIA string theory free energies to all orders in the $α'$ expansion. We discuss the implications of our results for holography and the physics of AdS$_4$ black holes.
