论文标题
$ \ Mathcal {n} = 2 $ super-$ \ Mathcal {w} _3 $全息词典上的注释
A note on the $\mathcal{N}=2$ super-$\mathcal{W}_3$ holographic dictionary
论文作者
论文摘要
这是一份长期过期的同伴论文：1512.00073。我们研究$ sl（3 | 2）$ CHERN-SIMONS SUPERGRAVITY在AD $ _3 $上的SuperGravity和$ \ Mathcal {n} = 2 $ super-super-$ \ nathcal {w} _3 $ symmetry。具体而言，我们在使超符号结构透明的基础上对渐近对称性进行了完整的分析，从而使我们能够在批量和边界对应物中建立电流和转换参数之间的精确字典。我们还讨论了来源的合并，并全面显示相应的全息病房身份。通过在CFT电流上施加合适的墓穴条件，我们将Superalgebra $ su（2,1 | 1,1）$确定为洛伦兹签名中$ SL（3 | 2）$的适当真实形式。我们借此机会回顾了$ \ Mathcal {n} = 2 $ super-$ \ $ \ Mathcal {w} _3 $共形代数的某些属性，包括其多重结构，OPE和光谱流量不变性，纠正文献中存在的一些次要次数。
This is a long-overdue companion paper to arXiv:1512.00073. We study the relation between $sl(3|2)$ Chern-Simons supergravity on AdS$_3$ and two-dimensional CFT's with $\mathcal{N}=2$ super-$\mathcal{W}_3$ symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in a basis that makes the superconformal structure transparent, allowing us to establish the precise dictionary between currents and transformation parameters in the bulk and their boundary counterparts. We also discuss the incorporation of sources and display in full detail the corresponding holographic Ward identities. By imposing suitable hermiticity conditions on the CFT currents, we identify the superalgebra $su(2,1|1,1)$ as the appropriate real form of $sl(3|2)$ in Lorentzian signature. We take the opportunity to review some of the properties of the $\mathcal{N}=2$ super-$\mathcal{W}_3$ conformal algebra, including its multiplet structure, OPE's and spectral flow invariance, correcting some minor typos present in the literature.
