Nuclear Physics B ( IF 2.5 ) Pub Date : 2020-07-03 , DOI: 10.1016/j.nuclphysb.2020.115104 Thomas Creutzig , Naoki Genra , Yasuaki Hikida , Tianshu Liu
W-algebras are constructed via quantum Hamiltonian reduction associated with a Lie algebra and an -embedding into . We derive correspondences among correlation functions of theories having different W-algebras as symmetry algebras. These W-algebras are associated to the same but distinct -embeddings.
For this purpose, we first explore different free field realizations of W-algebras and then generalize previous works on the path integral derivation of correspondences of correlation functions. For , there is only one non-standard (non-regular) W-algebra known as the Bershadsky-Polyakov algebra. We examine its free field realizations and derive correlator correspondences involving the WZNW theory of , the Bershadsky-Polyakov algebra and the principal -algebra. There are three non-regular W-algebras associated to . We show that the methods developed for can be applied straightforwardly. We briefly comment on extensions of our techniques to general .
中文翻译:
不同W代数对称性的CFT之间的对应关系
W代数是通过与李代数相关的量子哈密顿量约简来构造的 和 -嵌入 。我们推导具有不同W代数作为对称代数的理论的相关函数之间的对应关系。这些W代数与同一个 但与众不同 -嵌入。
为此,我们首先探索W代数的不同自由域实现,然后概括相关函数对应关系的路径积分推导的先前工作。对于,只有一种非标准(非常规)W代数,即Bershadsky-Polyakov代数。我们研究其自由场实现,并得出涉及WZNW理论的相关器对应关系。,Bershadsky-Polyakov代数和本金 -代数。与三个非正则W代数相关。我们证明了为可以直接应用。我们简要评论一下我们将技术扩展到常规。