arXiv 2002.125872020-02hep-th

具有不同W-代数对称性的CFTs之间的对应关系

Correspondences among CFTs with different W-algebra symmetry

Thomas Creutzig, Naoki Genra, Yasuaki Hikida, Tianshu Liu

备注：: 52 pages
DOI：: 10.1016/j.nuclphysb.2020.115104

摘要：

W-代数是通过与李代数$\mathfrak{g}$相关联的量子Hamilton约化和将$\mathfrak{sl}(2)$ -嵌入到$\mathfrak{g}$中来构造的。我们导出了具有不同W-代数作为对称代数的理论的关联函数之间的对应关系。这些W-代数关联到相同的$\mathfrak{g}$但不同的$\mathfrak{sl}(2)$ -嵌入。为此，我们首先探讨了W-代数的不同自由场实现，然后推广了以前关于关联函数对应的路径积分求导的工作。对于$\mathfrak{g}=\mathfrak{sl}(3)$，只有一个非标准（非正则）W-代数，称为Bershadsky-Polyakov代数。我们研究它的自由场实现，并推导出相关的对应关系涉及WZNW理论的$\mathfrak{sl}(3)$，Bershadsky-Polyakov代数和主$W_3$ -代数。有三个非正则W-代数与$\mathfrak{g}=\mathfrak{sl}(4)$相关联。我们表明，为$\mathfrak{g}=\mathfrak{sl}(3)$开发的方法可以直接应用。我们简要地评论我们的技术一般$\mathfrak{g}$的扩展。

英文摘要：

W-algebras are constructed via quantum Hamiltonian reduction associated with a Lie algebra $\mathfrak{g}$ and an $\mathfrak{sl}(2)$-embedding into $\mathfrak{g}$. We derive correspondences among correlation functions of theories having different W-algebras as symmetry algebras. These W-algebras are associated to the same $\mathfrak{g}$ but distinct $\mathfrak{sl}(2)$-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 $\mathfrak{g}=\mathfrak{sl}(3)$, 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 $\mathfrak{sl}(3)$, the Bershadsky-Polyakov algebra and the principal $W_3$-algebra. There are three non-regular W-algebras associated to $\mathfrak{g}=\mathfrak{sl}(4)$. We show that the methods developed for $\mathfrak{g}=\mathfrak{sl}(3)$ can be applied straightforwardly. We briefly comment on extensions of our techniques to general $\mathfrak{g}$.

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