论文标题
多矩阵型号的双缩放限制在大$ d $上
Double scaling limit of multi-matrix models at large $D$
论文作者
论文摘要
In this paper, we study a double scaling limit of two multi-matrix models: the $U(N)^2 \times O(D)$-invariant model with all quartic interactions and the bipartite $U(N) \times O(D)$-invariant model with tetrahedral interaction ($D$ being here the number of matrices and $N$ being the size of each matrix).这些型号承认是双重的，大的$ n $和大$ D $扩展。尽管$ n $跟踪了Feynman图的属，但$ d $跟踪了另一个称为The等级的数量。在这两个模型中，我们都将固定属的feynman图和等级的总和作为有限的总和，而不是组合对象。这是组合性质的结果，在量子机械环境和量子场理论中仍然是正确的。然后，我们以$ d $的大规模限制限制，即用于消失的等级。特别是，我们发现两种模型中最奇异的方案与Benedetti等人中的方案相同。对于$ u（n）^2 \ times o（d）$ - 不变模型仅限于其四面体交互。这是与1-matrix模型中的双重缩放类别相比，这是一个不同的通用类别。
In this paper, we study a double scaling limit of two multi-matrix models: the $U(N)^2 \times O(D)$-invariant model with all quartic interactions and the bipartite $U(N) \times O(D)$-invariant model with tetrahedral interaction ($D$ being here the number of matrices and $N$ being the size of each matrix). Those models admit a double, large $N$ and large $D$ expansion. While $N$ tracks the genus of the Feynman graphs, $D$ tracks another quantity called the grade. In both models, we rewrite the sum over Feynman graphs at fixed genus and grade as a finite sum over combinatorial objects called schemes. This is a result of combinatorial nature which remains true in the quantum mechanical setting and in quantum field theory. Then we proceed to the double scaling limit at large $D$, i.e. for vanishing grade. In particular, we find that the most singular schemes, in both models, are the same as those found in Benedetti et al. for the $U(N)^2 \times O(D)$-invariant model restricted to its tetrahedral interaction. This is a different universality class than in the 1-matrix model whose double scaling is not summable.
