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arXiv 2205.05091hep-th
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用扰动和畴壁方法研究$W_3$极小模型之间的PDKEEPAAA流动

RG flow between $W_3$ minimal models by perturbation and domain wall approaches

Hasmik Poghosyan, Rubik Poghossian

摘要:

我们探讨了具有$W_3$对称性的相邻极小CFT模型之间的RG流。在计算了几类OPE结构常数后,我们找到了三类RG不变局部场集的反常维数矩阵。第一类中的每个集合由单个主字段组成,第二个是三个主字段中的第二个,而第三类中的集合包含六个主字段和四个次字段。我们对角化他们的矩阵的异常尺寸和建立明确的映射之间的UV和IR领域(混合系数)。在研究二次场的三点函数时,我们遇到了一个有趣的现象,即全纯反全纯因式分解性质的破坏,这在只具有Virasoro对称性的普通极小模型中是不会发生的.此外,所考虑的扰动保持$W$变换的非平凡子群。我们明确地导出了相应的守恒电流。我们用这个电流定义了扰动理论中的反常$W$-权的概念:反常维数矩阵的类比。对于只有准素域的RG不变集,我们用结构常数导出了这个量的公式。这使我们能够明确地计算第一类和第二类的异常$W$权重。同样的RG流,我们调查也与域壁的方法为第二RG不变类,并找到完全一致的微扰方法。

英文摘要:

We explore the RG flow between neighboring minimal CFT models with $W_3$ symmetry. After computing several classes of OPE structure constants we were able to find the matrices of anomalous dimensions for three classes of RG invariant sets of local fields. Each set from the first class consists of a single primary field, the second one of three primaries, while sets in the third class contain six primary and four secondary fields. We diagonalize their matrices of anomalous dimensions and establish the explicit maps between UV and IR fields (mixing coefficients). While investigating the three point functions of secondary fields we have encountered an interesting phenomenon, namely violation of holomorphic anti-holomorphic factorization property, something that does not happen in ordinary minimal models with Virasoro symmetry solely. Furthermore, the perturbation under consideration preserves a non-trivial subgroup of $W$ transformations. We have derived the corresponding conserved current explicitly. We used this current to define a notion of anomalous $W$-weights in perturbed theory: the analog for matrix of anomalous dimensions. For RG invariant sets with primary fields only we have derived a formula for this quantity in terms of structure constants. This allowed us to compute anomalous $W$-weights for the first and second classes explicitly. The same RG flow we investigate also with the domain wall approach for the second RG invariant class and find complete agreement with the perturbative approach.

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