Duality and Confinement in 3d $\mathcal{N}=2$ "chiral" $SU(N)$ gauge theories

Abstract

We study low-energy dynamics of three-dimensional $\mathcal{N}=2$ $SU(N)$ "chiral" gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matters without a Chern-Simons term. Compared to a naive semi-classical analysis of the Coulomb branch, its quantum structure is highly richer than expected due to so-called "dressed" Coulomb branch (monopole) operators. We propose dualities and confinement phases for the "chiral" $SU(N)$ theories. The theories with $N>F>\bar{F}$ exhibit spontaneous supersymmetry breaking. The very many Coulomb branch operators generally remain exactly massless and are non-trivially mapped under the dualities. Some dualities lead to a novel duality between $SU(N)$ and $USp(2\tilde{N})$ theories. For the 3d $\mathcal{N}=2$ $SU(2)$ gauge theory with $2F$ doublets, there are generally $F+2$ "chiral" and "non-chiral" dual descriptions.

Appendix added, discussions added, references added

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• Seiberg Duality in Chern-Simons Theory
• Superconformal Indices for $\mathcal{N}=6$ Chern Simons Theories
• Generalized Superconformal Index for Three Dimensional Field Theories
• Dynamics of 3D SUSY Gauge Theories with Antisymmetric Matter
• $USp(2N_c)$ SQCD${}_3$ with antisymmetric: dualities and symmetry enhancements
• 3d s-confinement for three-index matters

Cited by in corpus (9)

• Generalized Giveon-Kutasov duality
• 3d "chiral" Kutasov-Schwimmer duality
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Monopoles and dualities in $3d$ $\mathcal{N}=2$ quivers
• Confinement in 3d $\mathcal{N}=2$ $Spin(N)$ gauge theories with vector and spinor matters
• 3d Self-Dualities
• 3d $Spin(N)$ Seiberg dualities
• Coulomb branch in 3d $\mathcal{N}=2$ $SU(N{)}_k$ Chern-Simons gauge theories with chiral matter content
• On s-confinement in 3d $\mathcal{N}=2$ gauge theories with anti-symmetric tensors