Advances in Theoretical and Mathematical Physics

Volume 25 (2021)

Number 8

Masses, sheets and rigid SCFTs

Pages: 1953 – 2054



Aswin Balasubramanian (NHETC and Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey, U.S.A.; and DESY (Theory) and Department of Mathematics, University of Hamburg, Germany)

Jacques Distler (Theory Group, Department of Physics, University of Texas, Austin, Tx., U.S.A.)


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