On large N limit of symmetric traceless tensor models
On large N limit of symmetric traceless tensor models
复制标题
对称无痕张量模型的大N极限
DOI：
10.1007/jhep10(2017)037
复制
发表时间：
2017
影响因子：
5.4
通讯作者：
G. Tarnopolsky
中科院分区：
文献类型：
--
作者：
I. Klebanov;G. Tarnopolsky
对于自由度为3或更高秩张量的某些理论，存在由Melonic图支配的可解大N极限。简单的例子是由包含一个秩3张量的三基本表示的O（N）3对称群的模型。当假设四次相互作用具有特殊的四面体指数结构时，耦合常数g必须标度为N− 3/2（在美仑大N极限下）。在本文中，我们考虑一个大N理论的一个完全对称和无痕的秩3张量与四面体四次相互作用的组合，这个模型有一个单一的O（N）对称群。我们明确地计算所有的真空图为了g 8，以及一些图的高阶，并发现，在大N限制，其中g 2 N 3是固定的，只有melonic图生存。虽然在O（N）对称理论中，一些非melonic图比O（N）3对称理论得到了增强，但我们还没有发现任何图的这种增强足以使它们与melonic图相媲美。受这些结果的启发，我们猜想一个真实的秩为3的对称无迹张量的模型具有一个光滑的大N极限，其中g2 N3保持不变，并且所有的贡献图都是melonic图.对称无迹张量模型的一个特征是，某些包含奇数个顶点的真空图相对于Melonic图仅被抑制了N− 1/2。
For some theories where the degrees of freedom are tensors of rank 3 or higher, there exist solvable large N limits dominated by the melonic diagrams. Simple examples are provided by models containing one rank 3 tensor in the tri-fundamental representation of the O (N) 3 symmetry group. When the quartic interaction is assumed to have a special tetrahedral index structure, the coupling constant g must be scaled as N− 3/2 in the melonic large N limit. In this paper we consider the combinatorics of a large N theory of one fully symmetric and traceless rank-3 tensor with the tetrahedral quartic interaction; this model has a single O (N) symmetry group. We explicitly calculate all the vacuum diagrams up to order g 8, as well as some diagrams of higher order, and find that in the large N limit where g 2 N 3 is held fixed only the melonic diagrams survive. While some non-melonic diagrams are enhanced in the O (N) symmetric theory compared to the O (N) 3 one, we have not found any diagrams where this enhancement is strong enough to make them comparable with the melonic ones. Motivated by these results, we conjecture that the model of a real rank-3 symmetric traceless tensor possesses a smooth large N limit where g 2 N 3 is held fixed and all the contributing diagrams are melonic. A feature of the symmetric traceless tensor models is that some vacuum diagrams containing odd numbers of vertices are suppressed only by N− 1/2 relative to the melonic graphs.
影响因子：
5
作者：
Maldacena, Juan;Stanford, Douglas
通讯作者：
Stanford, Douglas