Abstract
Recently a very interesting three-dimensional mathcal{N}=2 supersymmetric theory with SU(3) global symmetry was discussed by several authors. We denote this model by Tx. 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 Tx 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 mathcal{N}=2 mirror dualities involving such constructions with the dual being either a simple mathcal{N}=2 Wess-Zumino model or a discrete gauging thereof.
Highlights
3d/3d correspondence [11] in [12, 13]
We investigate models which can be constructed by using Tx as a building block gauging the global symmetry and paying special attention to the global structure of the gauge group
Another observation is that the basic monopole operators in many examples we study here are counted by Catalan numbers, and it would be interesting to understand whether mirror models with such property, that is Catalan numbers counting operators built from fundamental fields, can be considered
Summary
The first description has N = 1 supersymmetry and manifest SU(3) global symmetry. This is a Wess-Zumino model of eight real superfields with superpotential, dacbχaχbχc. Dabc = Tr Ta{Tb , Tc} with Ta the generators of SU(3). It was conjectured in [6, 7] that the supersymmetry of this model enhances to N = 2 and a continuous R-symmetry emerges in the IR CFT
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