关于BMS ${}_3$不变场论的注记：关联函数和非酉CFTs
Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
摘要：
我们使用BMS ${}_3$和$W(2,2)$代数之间的同构来重新考虑具有被定义为手征对称性的BMS ${}_3$代数的CFTs的一些通用方面。对于么正理论，已知扩展对称生成元的作用是平凡的，并且所得到的理论等价于仅具有Virasoro对称性的CFT。对于非酉CFTs，我们定义了一个依赖于幂零变量的算子，并通过这个新算子的作用来组织Verma模块。最后，我们找到了修正的沃德恒等式所施加的条件。
英文摘要：
We use the isomorphism between the BMS${}_3$ and the $W(2,2)$ algebras to reconsider some generic aspects of CFTs with the BMS${}_3$ algebra defined as a chiral symmetry. For unitarity theories, it is known that the extended symmetry generator acts trivially, and the resulting theory is equivalent to a CFT with a Virasoro symmetry only. For nonunitary CFTs, we define an operator depending on a nilpotent variable, and we organize the Verma module through the action of this new operator. Finally, we find the conditions imposed by the modified Ward identity.
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