Revisiting random tensor models at large N via the Schwinger-Dyson equations
Revisiting random tensor models at large N via the Schwinger-Dyson equations
复制标题
通过 Schwinger-Dyson 方程重新审视大 N 的随机张量模型
DOI：
10.1007/jhep03(2013)160
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发表时间：
2012
影响因子：
5.4
通讯作者：
V. Bonzom
中科院分区：
文献类型：
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作者：
V. Bonzom
矩阵模型的Schwinger-Dyson方程(SDE)构成(半)Virasoro代数，已成为求解矩阵模型的标准工具。由张量模型中的SDE生成的代数(对于适当系综中的随机张量)是Virasoro代数的具体推广，证明这些新的对称性决定了物理解是很重要的。对于大N的随机张量，我们证明了这一结果。与矩阵模型相比，张量模型在张量项的每一阶都有不止一个不变量，并且SDE使它们扩散。然而，主导观测的特定组合允许将其限制为线性SDE，并且我们证明了它们确定唯一的物理微扰解。这给出了一个新的证明，即张量模型是大N的高斯模型，协方差是全两点函数。
The Schwinger-Dyson Equations (SDEs) of matrix models are known to form (half) a Virasoro algebra and have become a standard tool to solve matrix models. The algebra generated by SDEs in tensor models (for random tensors in a suitable ensemble) is a specific generalization of the Virasoro algebra and it is important to show that these new symmetries determine the physical solutions. We prove this result for random tensors at large N. Compared to matrix models, tensor models have more than a single invariant at each order in the tensor entries and the SDEs make them proliferate. However, the specific combinatorics of the dominant observables allows to restrict to linear SDEs and we show that they determine a unique physical perturbative solution. This gives a new proof that tensor models are Gaussian at large N, with the covariance being the full 2-point function.