Dualities from dualities in 2d $\mathcal{N}=(0,2)$

TL;DR

This work extends the landscape of 2d $\mathcal{N}=(0,2)$ gauge/ LG dualities by deriving families of SU($N$) theories with antisymmetric matter and their Landau-Ginzburg duals through a 4d-to-2d topological-twist construction. Central to the construction is the tensor deconfinement mechanism, realized via USp(2n) sectors, which reshapes two-index tensors into fundamental representations and yields quiver descriptions that flow to LG models under basic dualities. The authors perform thorough checks, including 't Hooft anomaly matching and elliptic-genus identities, and demonstrate both 4d-origin dualities and genuinely new 2d dualities (some without obvious 4d parents). They also discuss subtleties of deconfinement in the presence of non-compact target spaces and the c-extremization framework, and provide explicit computations for representative models such as USp(4) with antisymmetric matter and two fundamentals. Overall, the paper strengthens the 4d–2d link for SUSY dualities, expands the 2d duality web with new models, and offers robust checks via sphere reductions, index identities, and LG realizations.

Abstract

We propose 2d $\mathcal{N}=(0,2)$ dualities between SU(N) gauge theories with fundamental and antisymmetric chiral matter and Landau-Ginzburg theories with chiral and Fermi multiplets. Many of these dualities can be derived by topologically twisting 4d s-confining gauge theories on a two-sphere, with integer non-negative $R$ charges. We provide various checks of the dualities, showing that they descend from more "basic" dualities, similarly to analogous derivations in higher dimensions. The proof are based on the fact that the antisymmetric tensors can be traded with USp(2n) gauge theories with fundamental chirals, mimicking the higher dimensional mechanism known as tensor deconfinement. The quivers obtained in this way can be shown to be dual to LG models after applying other elementary "basic" dualities.

Figures (16)

• Figure 1: General quiver for the models studied in this section. $N=2n$ in \ref{['Case1even']}, \ref{['Case2even']} and \ref{['Case3even']}; $N=2n+1$ in \ref{['Case1odd']}, \ref{['Case2odd']} and \ref{['Case3odd']}. $M=0,\,1,\,2$.
• Figure 2: The first quiver represents the $\mathop{\mathrm{SU}}\nolimits(2n)$ gauge theory with an antisymmetric $A$, $2n$ anti-fundamentals $\tilde{Q}$ and two fundamentals $Q$. The second quiver is obtained by trading the antisymmetric $A$ and the two fundamentals $Q$ with an auxiliary $\mathop{\mathrm{USp}}\nolimits(2n)$ gauge node with the bifundamental $P$ and the fundamentals $R$. The third quiver is obtained by dualizing the $\mathop{\mathrm{SU}}\nolimits(2n)$ node into a LG theory. Observe that in the quivers we did not represent the singlets that arise in the various steps, as they are discussed in detail in the discussion appearing in the paper.
• Figure 3: The first quiver represents the $\mathop{\mathrm{SU}}\nolimits(2n+1)$ gauge theory with an antisymmetric $A$, $2n+1$ anti-fundamentals $\tilde{Q}$ and two fundamentals $Q_{1,2}$. Observe that we split these two fundamentals in the figure because in the second quiver we traded the antisymmetric $A$ and just one of these two fundamentals (here $Q_1$) with an auxiliary $\mathop{\mathrm{USp}}\nolimits(2n)$ gauge node with the bifundamental $P$ and the fundamental $R$. The third quiver is obtained by dualizing the $\mathop{\mathrm{SU}}\nolimits(2n+1)$ node into a LG theory. Again we did not represent the various singlets in these figures.
• Figure 4: The first quiver represents the $\mathop{\mathrm{SU}}\nolimits(2n+1)$ gauge theory with an antisymmetric $A$, $2n$ anti-fundamentals $\tilde{Q}$ and three fundamentals $Q$. In the second quiver we exchanged the antisymmetric $A$ and the three fundamentals with an auxiliary $\mathop{\mathrm{USp}}\nolimits(2n)$ gauge node with the bifundamental $P$ and the fundamentals $R$. In this case we also represent the Fermi field $\Psi_R$ in the figure, in the anti-fundamental (if we want to write a J-term in the action) representation of the $\mathop{\mathrm{SU}}\nolimits(3)$ flavor symmetry. In this case we did not represent a third quiver obtained by dualizing the $\mathop{\mathrm{SU}}\nolimits(2n+1)$ node.
• Figure 5: The first quiver represents the $\mathop{\mathrm{SU}}\nolimits(2n)$ gauge theory with an antisymmetric $A$, $2n-2$ anti-fundamentals $\tilde{Q}$ and four fundamentals $Q$. In the second quiver we exchanged the antisymmetric $A$ and the four fundamentals with an auxiliary $\mathop{\mathrm{USp}}\nolimits(2n+2)$ gauge node with the bifundamental $P$ and the fundamentals $R$. In this case we also represent the Fermi field $\Psi_R$ in the figure, in the antisymmetric representation of the $\mathop{\mathrm{SU}}\nolimits(4)$ flavor symmetry. In the third quiver we represent the theory obtained after the duality on $\mathop{\mathrm{SU}}\nolimits(2n)$, that gives an $\mathop{\mathrm{SU}}\nolimits(2)$ gauge theory. Then the fourth quiver is obtained by dualizing $\mathop{\mathrm{USp}}\nolimits(2n+2)$, leaving just an $\mathop{\mathrm{SU}}\nolimits(2)$ gauge theory. Observe that in this case we represented in the various quivers the gauge singlets in non-trivial representations of the flavor symmetry group, while the others are omitted and can be found in the discussion in the body of the paper.