Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces
Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces
复制标题
从矩阵模型的角度看张量模型：随机表面上的循环模型的情况
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
F. Combes
中科院分区：
文献类型：
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作者：
V. Bonzom;F. Combes
我们通过$U(\tau)$矩阵模型研究了随机张量和随机矩阵之间的联系，该模型在随机表面上生成了完全填充的、定向的环路。后者被发现与一组通常在张量模型中发现的规则边彩色图双射。结果表明，环数的展开式类似于三阶张量模型的1/N展开式。本文综述了张量模型的最新研究成果，并将其应用于此。例如，使环路数量最大化的构型正是张量模型的单调图，并且找到了投影到单调扇区上的缩放极限。我们还从随机曲面上的环的角度重新解释了张量模型的双尺度极限。这种方法最终被推广到高阶张量模型，它在维度d-1的三角上产生具有逸度的循环。
We study a connection between random tensors and random matrices through $U(\tau)$ matrix models which generate fully packed, oriented loops on random surfaces. The latter are found to be in bijection with a set of regular edge-colored graphs typically found in tensor models. It is shown that the expansion in the number of loops is organized like the 1/N expansion of rank-three tensor models. Recent results on tensor models are reviewed and applied in this context. For example, configurations which maximize the number of loops are precisely the melonic graphs of tensor models and a scaling limit which projects onto the melonic sector is found. We also reinterpret the double scaling limit of tensor models from the point of view of loops on random surfaces. This approach is eventually generalized to higher-rank tensor models, which generate loops with fugacity $\tau$ on triangulations in dimension $d-1$.