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

TL;DR

The paper addresses the role of zero-form and one-form global symmetries in 3d ${ m ABJ/ABJM}$-type theories with ${ m N}\ge 6$ SUSY, showing that gauging one-form symmetries generates new dual pairs between orthosymplectic and unitary gauge theories. It employs refined ${ m 3d}$ superconformal indices to map discrete symmetry data, mixed anomalies, and topological sectors across dual frames, revealing intricate symmetry matchings and, in some cases, trivial actions of certain higher-form symmetries on line spectra. The main results include a network of dualities such as ${ m SO}(2N)_2 imes{ m USp}(2N)_{-1}/\\mathbb{Z}_2$ ⇄ ${[{ m U}(N)_4 imes{ m U}(N)_{-4}]/\mathbb{Z}_4}$ and related quotients, as well as a generalization to circular quivers dual to Kronheimer–Nakajima quivers whose Higgs or Coulomb branches realize instantons on orbifolds. The findings clarify global structures in ABJ/ABJM dualities, illustrate how higher-form symmetries are encoded in the index, and open avenues for gravity duals and broader generalizations of discrete symmetries in 3d SCFTs.

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.