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Correspondences among CFTs with different W-algebra symmetry
Nuclear Physics B ( IF 2.8 ) 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 g and an sl(2)-embedding into g. We derive correspondences among correlation functions of theories having different W-algebras as symmetry algebras. These W-algebras are associated to the same g but distinct 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 g=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 sl(3), the Bershadsky-Polyakov algebra and the principal W3-algebra. There are three non-regular W-algebras associated to g=sl(4). We show that the methods developed for g=sl(3) can be applied straightforwardly. We briefly comment on extensions of our techniques to general g.



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 Gsl2-嵌入 G。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G 但与众不同 sl2-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G=sl3,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。sl3,Bershadsky-Polyakov代数和本金 w ^3-代数。与三个非正则W代数相关G=sl4。我们证明了为G=sl3可以直接应用。我们简要评论一下我们将技术扩展到常规G

更新日期:2020-07-13
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