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

References in corpus (12)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Generalized Global Symmetries
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Fractional M2-branes
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• AdS_4/CFT_3 -- Squashed, Stretched and Warped
• Generalized symmetries and holography in ABJM-type theories
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
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