Chiral 3d SU(3) SQCD and $$ \mathcal{N}=2 $$ mirror duality

Abstract

Recently a very interesting three-dimensional N = 2 supersymmetric theory with SU(3) global symmetry was discussed by several authors. We denote this model by T x. This was conjectured to have two dual descriptions, one with explicit supersymmetry and emergent flavor symmetry and the other with explicit flavor symmetry and emergent supersymmetry. We discuss a third description of the model which has both flavor symmetry and supersymmetry manifest. We then investigate models which can be constructed by using T x as a building block gauging the global symmetry and paying special attention to the global structure of the gauge group. We conjecture several cases of N = 2 mirror dualities involving such constructions with the dual being either a simple N = 2 Wess-Zumino model or a discrete gauging thereof.

A tale of exceptional 3d dualities

“…In the case of minimal number of colors for the gauge groups, N c = 1, it is possible to flow to various new dualities and also to many known, apparently unrelated, N = 2 dualities, that appeared scattered in the literature. As far as we know, all studied dualities relating theories with rank-1 or rank-0 gauge groups are obtained: 1 the mirror of U(1) with 2 or 1 flavors [12], Aharony dualities [13] for U(1) with 2 flavors and Usp(2) = SU(2) with 6 or 4 doublets and their real mass deformations [14][15][16], the mirror of U(1) 1 2 with 1 chiral flavor [17], the dual of U(1) W=M + +M − , 4 [18] or 3 [19] flavors, the dual of U(1) W=M + , 3 [20] or 2 [20,21] flavors, a duality "SU(2) 1 with 4 doublets" ↔ "U(1) with 2 flavors" [22,23] (which explains IR symmetry enhancement in the latter model [24]), a duality "U(1) 3 2 ,W=M + with 3 chiral flavors" ↔ "U(1) with 2 chiral flavors" [25] (which explains IR symmetry enhancement in the latter model [24][25][26][27][28]).…”

Supersymmetric indices of 3d S-fold SCFTs

“…Since the coefficient of x 2 counts the number of marginal operators minus the number of conserved currents [44,49] (see also [51]), there must be two extra conserved currents associated with the terms − (ω + ω −1 ) x 2 . Such extra conserved currents come from two N = 3 extra SUSY-current multiplets A 2 [0]…”

“…Although the brane configuration for n > 1 is not known, we demonstrate below that such theories have interesting properties from the field theoretic perspective. The indices involving SU (N )/Z N gauge group for theories in 3d were discussed in [44,57] 15 . Here, we write down the expression of the index for (6.1), analogous to those presented in [44]: 16…”

Marginal deformations of 3d $$ \mathcal{N} $$ = 4 linear quiver theories

“…We already alluded to this fact when explaining why the 3d N = 2 superconformal manifold has the structure of a momentmap quotient [13]. If the global symmetries of the SCFT are known (they are not always manifest), one can extract unambiguously its marginal deformations from the index (see e.g., [45,46] for applications). 9 The A-type multiplets do not contribute to the chiral ring, since none has scalar states that saturate the BPS bound (i.e.…”