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# Advances in Theoretical and Mathematical Physics

## Volume 25 (2021)

### Number 8

### Masses, sheets and rigid SCFTs

Pages: 1953 – 2054

DOI: https://dx.doi.org/10.4310/ATMP.2021.v25.n8.a1

#### Authors

#### Abstract

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.

Published 14 September 2022