Zero-form and one-form symmetries of the ABJ and related theories

Abstract

The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis (ABJ) and related theories, with at least $\mathcal{N}=6$ supersymmetry in three dimensions, are examined in detail. Starting from well-known dualities between theories with orthogonal and symplectic gauge groups and those with unitary gauge groups, we gauge their one-form symmetries or their subgroups and obtain new dualities. One side of the latter involves theories with special orthogonal and symplectic gauge groups, and the other side involves theories with unitary gauge groups; there is a discrete quotient on one or both sides of the duality. We study the refined superconformal indices of such theories and map the symmetries across the dualities, with particular attention to their discrete part. As a generalisation, we also find a new duality between a circular quiver with a discrete quotient of alternating special orthogonal and symplectic gauge groups and a three-dimensional $\mathcal{N}=4$ circular (Kronheimer-Nakajima) quiver with unitary gauge groups, whose Higgs or Coulomb branch describes an instanton on a singular orbifold.

46 pages; v2: comments added

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Cited by in corpus (13)

• The Branes Behind Generalized Symmetry Operators
• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Symmetry TFTs for 3d QFTs from M-theory
• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Subsystem Non-Invertible Symmetry Operators and Defects
• Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
• Anomalies of Generalized Symmetries from Solitonic Defects
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Dualities and flavored indices of M2-brane SCFTs
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories