论文标题
Melonic CFT
Melonic CFTs
论文作者
论文摘要
Melonic限制是一种相对较新的大型$ N $限制，与较旧且众所周知的大$ n $限制的矢量和矩阵场理论不同，分别由仙人掌和平面Feynman图所主导。 Melonic限制通常出现在张量场理论中，其特征是一个不变性组，其中该字段转换为$ r $ r $不同简单的Lie Groups的$ r \ geq 3 $基本表示的产物。顾名思义，在这种限制下，自由能和相关因子的扰动扩展由旋律图主导。后者构成了平面图的可管理子集，但结构比仙人掌图更丰富，因此它们开放了以受控方式研究的可能性，其重新规范化组的固定点的新类型。我们称\ emph {melonic共形场理论（CFTS）}在旋速限制中发现的那些定点理论。我们简单地回顾了$ d \ geq 2 $（Euclidean）时空维度的张量现场理论的构建和分析，并特别强调了一般的理论框架，以及某些模型的固定点的具体结果。
The melonic limit is a relatively new type of large-$N$ limit, differing from the much older and well-known large-$N$ limits of vector and matrix field theories, which are dominated by cactus and planar Feynman diagrams, respectively. The melonic limit typically appears in tensor field theories, characterized by an invariance group in which the fields transform as the product of $r\geq 3$ fundamental representations of $r$ different simple Lie groups. As the name suggests, in such a limit the perturbative expansion of free energy and correlators are dominated by melonic diagrams. The latter form a manageable subset of the planar diagrams, but with a richer structure than cactus diagrams, and therefore they open the possibility of studying in a controlled manner new types of fixed points of the renormalization group. We call \emph{melonic conformal field theories (CFTs)} those fixed-point theories that are found in the melonic limit. We concisely review the construction and analysis of tensor field theories in $d\geq 2$ (Euclidean) spacetime dimensions, with special emphasis on the general theoretical framework, and on specific results for the fixed points of some models.
