Rectangular W algebras and superalgebras and their representations
Rectangular W algebras and superalgebras and their representations
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DOI：
10.1103/physrevd.100.086008
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发表时间：
2019-06
影响因子：
5
通讯作者：
T. Creutzig;Yasuaki Hikida
中科院分区：
文献类型：
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作者：
T. Creutzig;Yasuaki Hikida
我们研究通过与矩形类型的$sl(2)$嵌入相关的$sl(Mn)$的量子哈密顿约化得到的W - 代数。该代数可实现为具有$M\times M$矩阵值场的高自旋引力的渐近对称性。在我们之前的工作中，我们研究了W - 代数的基本性质，并声称基于全息原理的一个提议，即使在有限中心荷的情况下，该代数也可实现为类格拉斯曼陪集的对称性。在本文中，我们通过以下方式扩展分析。首先，我们计算低自旋生成元之间的算符乘积展开，去除$n = 2$的限制。其次，我们通过几种方式研究简并表示，并考察与陪集谱以及高自旋引力的锥形缺陷几何的关系。对于这些分析，我们主要设定$M = n = 2$。最后，我们通过引入$\mathcal{N}=2$超对称性扩展之前的分析。
We study W-algebras obtained by quantum Hamiltonian reduction of $sl(Mn)$ associated to the $sl(2)$ embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued fields. In our previous work, we examined the basic properties of the W-algebra and claimed that the algebra can be realized as the symmetry of Grassmannian-like coset even with finite central charge based on a proposal of holography. In this paper, we extend the analysis in the following ways. First, we compute the operator product expansions among low spin generators removing the restriction of $n = 2$. Second, we investigate the degenerate representations in several ways, and see the relations to the coset spectrum and the conical defect geometry of the higher spin gravity. For these analyses, we mainly set $M=n=2$. Finally, we extend the previous analysis by introducing $\mathcal{N}=2$ supersymmetry.