论文标题
具有不同W-Algebra对称性的CFT之间的对应关系
Correspondences among CFTs with different W-algebra symmetry
论文作者
论文摘要
W-Algebras是通过与Lie代数$ \ Mathfrak {G} $和$ \ Mathfrak {SL}（2）$相关的量子Hamiltonian还原构建的。我们得出具有不同W-代数作为对称代数的理论的相关函数之间的对应关系。这些W-Algebras与相同的$ \ Mathfrak {G} $相关联，但$ \ Mathfrak {Sl}（2）$ - 嵌入。 为此，我们首先探索W-Algebras的不同自由场实现，然后概括有关相关函数对应关系的路径积分的先前工作。对于$ \ mathfrak {g} = \ mathfrak {sl}（3）$，只有一个非标准（非规范）W-Algebra被称为Bershadsky-Polyakov代数。我们检查了其自由场实现，并得出了涉及$ \ mathfrak {SL}（3）$的WZNW理论，Bershadsky-Polyakov代数和主要$ W_3 $ -Algebra的wznw理论。与$ \ mathfrak {g} = \ mathfrak {sl}（4）$相关的三个非规范w-algebras。我们表明，为$ \ mathfrak {g} = \ mathfrak {sl}（3）$开发的方法可以直接应用。我们简要评论到一般$ \ mathfrak {g} $的扩展。
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 $\mathfrak{g}$.
