论文标题
伽利略CFT $ _2 $的影子形式主义
The Shadow Formalism of Galilean CFT$_2$
论文作者
论文摘要
在这项工作中，我们为二维伽利略形式理论（GCFT $ _2 $）开发了影子形式主义。我们定义了加利利形式对称组的主要序列表示，并找到与Wigner分类的关系，然后我们确定本地运算符的阴影变换。使用这种形式主义，我们得出了OPE块，Clebsch-Gordan内核，共形块和形式的局部波。一个新功能是，保形块允许其他分支点，这将破坏某些参数的OPE的收敛性。我们建立了另一个与上一个不同的反演公式，但是在分解平均场理论（MFT）中的四点函数时获得相同的结果。我们还构建了MFT的一系列连续的双向作用，以及一系列特殊的局部动作，其中之一是BMS自由标量模型。我们注意到，加利利形成对称性的外部自动形态，GCFT $ _2 $可以被视为较高维CFT的无效缺陷。
In this work, we develop the shadow formalism for two-dimensional Galilean conformal field theory (GCFT$_2$). We define the principal series representation of Galilean conformal symmetry group and find its relation with the Wigner classification, then we determine the shadow transform of local operators. Using this formalism we derive the OPE blocks, Clebsch-Gordan kernels, conformal blocks and conformal partial waves. A new feature is that the conformal block admits additional branch points, which would destroy the convergence of OPE for certain parameters. We establish another inversion formula different from the previous one, but get the same result when decomposing the four-point functions in the mean field theory (MFT). We also construct a continuous series of bilocal actions of MFT, and an exceptional series of local actions, one of which is the BMS free scalar model. We notice that there is an outer automorphism of the Galilean conformal symmetry, and the GCFT$_2$ can be regarded as null defect in higher dimensional CFTs.
