New 2d $\mathcal{N}=(0,2)$ dualities from four dimensions

Abstract

We propose some new infra-red dualities for $2d$ $\mathcal{N}=(0,2)$ theories. The first one relates a $USp(2N)$ gauge theory with one antisymmetric chiral, four fundamental chirals and $N$ Fermi singlets to a Landau-Ginzburg model of $N$ Fermi and $6N$ chiral fields with cubic interactions. The second one relates $SU(2)$ linear quiver gauge theories of arbitrary length $N-1$ with the addition of $N$ Fermi singlets for any non-negative integer $N$. They can be understood as a generalization of the duality between an $SU(2)$ gauge theory with four fundamental chirals and a Landau-Ginzburg model of one Fermi and six chirals with a cubic interaction. We derive these dualities from already known $4d$ $\mathcal{N}=1$ dualities by compactifications on ${\mathbb{S}}^2$ with suitable topological twists and we further test them by matching anomalies and elliptic genera. We also show how to derive them by iterative applications of some more fundamental dualities, in analogy with similar derivations for parent dualities in three and four dimensions.

38 pages, 11 figures; v2: typo correction; v3: revised version, published on JHEP

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• Boundary confining dualities and Askey-Wilson type $q$-beta integrals
• Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ dualities
• 3d exceptional gauge theories and boundary confinement
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• 2d dualities from 4d
• Sequential deconfinement in $3d$ $\mathcal{N}=2$ gauge theories
• Supersymmetric zeta functions and determinants
• Aspects of 4d supersymmetric dynamics and geometry