论文标题
Sachdev-ye-Kitaev模型的组合方面
Combinatorial aspects of the Sachdev-Ye-Kitaev model
论文作者
论文摘要
Sachdev-Ye-Kitaev（Syk）模型是$ q $交互的模型，其大n限制由旋速图主导。在这篇综述中，我们首先通过对其图形的直接组合分析进行了图表证明。然后，Gross和Rosenhaus提出了SYK模型的概括，该模型涉及带有不同风味的费米子。就Feynman图而言，这些口味可以看作是让人联想到随机张量理论中使用的颜色。可以识别现代工具从随机张量到这样的彩色SYK模型，可以识别大型$ N $扩展中2分和4分函数的所有领先和次要订单图。然后，我们在SYK模型的复杂，有色版本中研究非高斯平均值对随机耦合的影响。使用Polchinski样方程和随机张量高斯的普遍性，我们表明这种非高斯平均的效果导致修改了$ n $中领先顺序的高斯耦合分布的差异。然后，我们将有效行动的形式得出所有订单。
The Sachdev-Ye-Kitaev (SYK) model is a model of $q$ interacting fermions whose large N limit is dominated by melonic graphs. In this review we first present a diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs. Gross and Rosenhaus have then proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, these flavors can be seen as reminiscent of the colors used in random tensor theory. Applying modern tools from random tensors to such a colored SYK model, all leading and next-to-leading orders diagrams of the 2-point and 4-point functions in the large $N$ expansion can be identified. We then study the effect of non-Gaussian average over the random couplings in a complex, colored version of the SYK model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in $N$. We then derive the form of the effective action to all orders.
