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

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arxiv 2112.09531 v2 pith:PBLZCT65 submitted 2021-12-17 hep-th

Emanuele Beratto , Noppadol Mekareeya , Matteo Sacchi This is my paper · ORCID
classification hep-th
keywords gaugegroupstheoriessymmetriesdiscretedualitiesone-formorthogonal
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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.

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Cited by 2 Pith papers

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  1. Generalised global symmetries in 5d $\mathcal{N}=1$ theories from the blow-up equations

    hep-th 2026-07 conditional novelty 7.0 of 10

    Fractional exponents of the blow-up prefactor exp(-V_n) on 1-form backgrounds encode cubic and mixed anomalies of 5d N=1 SCFTs, deciding 2-groups versus mixed anomalies once the faithful UV symmetry is known from the index.

  2. Classification of Minimal Abelian Coulomb Branches

    hep-th 2024-12 conditional novelty 7.0 of 10

    Abelian 3d N=4 quivers with isolated Coulomb branch singularities are exactly stable chains and well-defined cycles, with geometries given by U(1) or finite cyclic quotients.

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