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 $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 4 circular (Kronheimer-Nakajima) quiver with unitary gauge groups, whose Higgs or Coulomb branch describes an instanton on a singular orbifold.

Dualities and flavored indices of M2-brane SCFTs

“…As discussed in section 2.1, this is dual to the (SU (2) 4 × SU (2) −4 )/Z 2 BLG theory.6.2.10 O(2) 2 × U Sp(2) −1 ABJThe index of the SO(2) 2 × U Sp(2) −1 ABJ theory with (ζ, χ) = (+, +) coincides with the index (6.13) for the U (1) 2 × U (1) −2 ABJM theory. This implies the duality (2.30)[21]. Thus it yields the Hilbert series(3.35) for C 2 /Z 2 in the Coulomb and Higgs limits.…”

“…The index of the resulting (SO(2) 2 × U Sp(2) −1 )/Z 2 ABJ theory matches with the index(3.18). This implies the duality (2.31)[21].…”

“…While the flavored indices of the ABJ(M) theory and BLG theory were computed in vast literature e.g. [15,[19][20][21], those of the N = 4 ADHM theories and their cousin have not yet been fully computed. 1 We find precise agreement of flavored indices as strong evidence of the conjectural dualities of M2-brane SCFTs including ADHM theory and other descriptions by comparing a large number of terms by expanding the flavored indices.…”

Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices

“…First we consider the SO(2N ) 2k × USp(2M ) −k version of the theory. This has a Z [1] 2 one-form symmetry coming from the diagonal combination of the centres of the two gauge nodes 24 (see [94,109]). There are also the Z 2 zero-form magnetic and charge conjugation symmetries.…”

“…(1. 5) This means that after gauging a Z The superconformal index in three dimensions is also sensitive to one-form symmetries, a fact that was already exploited for example in [93,94]. In particular, it depends on the global structure of the gauge group thorugh the summation over monopole sectors, which can be changed when gauging a one-form symmetry.…”