We study mass deformations of certain three-dimensional $\mathcal{N}=4$ Superconformal Field Theories (SCFTs) that have come to be called $T^\rho [G]$ theories. These are associated to tame defects of the six dimensional $(0, 2)$ SCFT $X[\mathfrak{j}]$ for $\mathfrak{j}=A,D,E$. We describe these deformations using a refined version of the theory of sheets, a subject of interest in Geometric Representation Theory. In mathematical terms, we parameterize local mass-like deformations of the tamely ramified Hitchin integrable system and identify the subset of the deformations that do admit an interpretation as a mass deformation for the theories under consideration. We point out the existence of non-trivial Rigid SCFTs among these theories. We classify the Rigid theories within this set of SCFTs and give a description of their Higgs and Coulomb branches. We then study the implications for the endpoints of RG flows triggered by mass deformations in these 3d $\mathcal{N}=4$ theories. Finally, we discuss connections with the recently proposed idea of Symplectic Duality and describe some conjectures about its action.

中文翻译：

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质量、片材和刚性 SCFT

我们研究某些三维 $\mathcal{N}=4$ 超共形场理论 (SCFT) 的质量变形，这些理论后来被称为 $T^\rho [G]$ 理论。这些与 $\mathfrak{j}=A,D,E$ 的六维 $(0, 2)$ SCFT $X[\mathfrak{j}]$ 的驯服缺陷有关。我们使用薄片理论的改进版本来描述这些变形，这是几何表示理论中感兴趣的主题。在数学术语中，我们参数化了驯服的 Hitchin 可积系统的局部质量状变形，并确定了变形的子集，这些变形的子集可以解释为正在考虑的理论的质量变形。我们指出了非平凡的刚性 SCFT的存在在这些理论中。我们在这组 SCFT 中对刚体理论进行分类，并描述它们的希格斯和库仑分支。然后，我们研究了在这些 3d $\mathcal{N}=4$ 理论中由质量变形触发的 RG 流端点的含义。最后，我们讨论了与最近提出的辛对偶概念的联系，并描述了一些关于其作用的猜想。