arXiv 1709.073662017-09hep-thmath-phmath.MP

一般矩阵-张量模型的一种新的大N展开式

A New Large N Expansion for General Matrix-Tensor Models

Frank Ferrari, Vincent Rivasseau, Guillaume Valette

备注：: 57 pages, 20 figures (additional discussion in Sec. 4.1.1. and additional figure (Fig. 5))

摘要：

我们定义了一个新的大$N$限制一般$\text{O}(N)^{R}$或$\text{U}(N)^{R}$不变张量模型，基于一个增强的大$N$缩放的耦合常数。由此产生的大的$N$扩展是按照与费曼图相关的半整数组织的，我们称之为索引。这个指数有一个自然的解释，在许多矩阵模型嵌入在张量模型。我们的新的缩放可以被证明是最佳的广泛的一类非melonic相互作用，其中包括所有的最大单迹项。我们的建设允许定义一个新的大$D$扩展的总和超过图的固定属矩阵模型与额外的$\text{O}(D)^{r}$全球对称性。当相互作用是$R+1$阶的完全顶点时，我们详细地确定了$R$是素数的导阶图.这个稍微令人惊讶的条件相当于完整的相互作用是最大的单迹。

英文摘要：

We define a new large $N$ limit for general $\text{O}(N)^{R}$ or $\text{U}(N)^{R}$ invariant tensor models, based on an enhanced large $N$ scaling of the coupling constants. The resulting large $N$ expansion is organized in terms of a half-integer associated with Feynman graphs that we call the index. This index has a natural interpretation in terms of the many matrix models embedded in the tensor model. Our new scaling can be shown to be optimal for a wide class of non-melonic interactions, which includes all the maximally single-trace terms. Our construction allows to define a new large $D$ expansion of the sum over diagrams of fixed genus in matrix models with an additional $\text{O}(D)^{r}$ global symmetry. When the interaction is the complete vertex of order $R+1$, we identify in detail the leading order graphs for $R$ a prime number. This slightly surprising condition is equivalent to the complete interaction being maximally single-trace.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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