We study global subalgebras of superconformal algebras in two dimensions and their unitary representations. Global superconformal multiplets are decomposed into conformal multiplets using Racah-Speiser algorithm, revealing many essential aspects of superconformal theories such as stress-energy tensor, conserved current, supersymmetric deformation and supersymmetry enhancement. Character formulae for the representations are presented. We further find a collection of conserved charges that are k-forms under the R-symmetry, which must be part of the super Virasoro algebra with $\mathcal{N}\ge 3$ supersymmetries.

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关于二维超保形表示的注释

我们研究二维的超共形代数的全局子代数及其单位表示。使用Racah-Speiser算法将整体超共形多重体分解为共形多重体，揭示了超共形理论的许多基本方面，例如应力-能量张量，守恒电流，超对称变形和超对称性增强。介绍了表示的字符公式。我们进一步找到了在R对称下为k形式的守恒电荷的集合，该守恒电荷必须是具有以下特征的超维拉索罗代数的一部分$\mathcal{ñ}\ge 3$ 超对称。