论文标题
Feigin-Semikhatov的W-Algebras和5D AGT对应的量子变形与简单的表面操作员
Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator
论文作者
论文摘要
$ gl_1 $的量子环形代数提供了许多与A型代数相关的变形W- algebras。这些代数有望与5D AGT对应关系相关。在本文中，我们讨论了从$ \ wideHat {su}（n）$获得的量子变形的量子变形，并通过su（2）嵌入[n-1,1]的量子Drinfeld-Sokolov还原。 Feigin和Semikhatov对他们进行了研究，我们将其称为Feigin-Semikhatov的W-Algebras。我们构建自由领域实现并找到几个二次关系。我们还将Whittaker状态的规范与在n = 3情况下的简单表面操作员存在下的intsanton分区函数进行了比较。
The quantum toroidal algebra of $gl_1$ provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed W-algebras including non-principal cases are obtained by gluing the quantum toroidal algebras of $gl_1$. These algebras are expected to be related with 5d AGT correspondence. In this paper, we discuss quantum deformation of the W-algebras obtained from $\widehat{su}(N)$ by the quantum Drinfeld-Sokolov reduction with su(2) embedding [N-1,1]. They were studied by Feigin and Semikhatov and we refer to them as Feigin-Semikhatov's W-algebras. We construct free field realization and find several quadratic relations. We also compare the norm of the Whittaker states with the instanton partition function under the presence of a simple surface operator in the N=3 case.
