Six Easy Pieces: interplays among dualities in 4d, 3d and 2d

TL;DR

This paper builds a bridge from 4d ${\rm SU}(N)$ gauge theories with a conjugate two-index antisymmetric tensor to a web of dual descriptions involving ${\rm USp}$ and ${\rm SO}$ gauge groups, mediated by tensor deconfinement and baryonic deformations. It shows that the 4d mixed-phase dynamics flow to non-Abelian Coulomb and magnetic free phases, revealing IR duals to ${\rm USp}(2M)$ SQCD, which descend to nontrivial 3d and 2d dualities. The authors derive and validate 3d dualities via three-sphere partition functions and the duplication formula, and they organize a unified picture linking SU with symmetric tensors to orthogonal duals after reductions. In 2d, they classify reductions into several cases with/without charged Fermi fields, identifying both known and new dualities and illustrating the robustness of tensor-deconfinement-based constructions. The work therefore provides a comprehensive, dimension-spanning framework for dualities among ${\rm SU}$, ${\rm USp}$, and ${\rm SO}$ gauge theories with tensor matter, and it opens avenues for further 4d–3d–2d connections and new tensor-flavor dualities.

Abstract

In this paper we consider 4d $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an interacting non-Abelian Coulomb phase and a free magnetic phase. Through tensor deconfinement, we show that baryonic deformations lead to a non-Abelian free magnetic phase. Along the analysis we obtain a duality with symplectic SQCD that can be further reduced to 3d and 2d. In the 3d case the analysis of the three sphere partition function allows one to obtain dualities between $\mathrm{SU}(N)$ with a two index symmetric tensor and $\mathrm{SO}(N)$ theories. On the other hand, in 2d we recover dualities already known in the literature and propose new ones between special unitary and symplectic gauge theories.

Figures (20)

• Figure 1: Quiver representation of the deconfinement of the conjugate antisymmetric in the presence of the deformation $W_{\text{ele}}=\tilde{A}^n$, using an $\mathop{\mathrm{USp}}\nolimits(2n-4)$ gauge group, followed by an ordinary Seiberg duality for the $\mathop{\mathrm{SU}}\nolimits(2n)$ gauge node.
• Figure 2: Quiver representation of the deconfinement of the conjugate antisymmetric in the presence of the deformation $W_{\text{ele}}=\tilde{A}^{n-1}\tilde{Q}_1\tilde{Q}_2$, using an $\mathop{\mathrm{USp}}\nolimits(2n-2)$ gauge group, followed by an ordinary Seiberg duality for the $\mathop{\mathrm{SU}}\nolimits(2n)$ gauge node.
• Figure 3: Quiver representation of the deconfinement of the conjugate antisymmetric in the presence of the deformation $W_{\text{ele}}=\tilde{A}^{n-2}\tilde{Q}_1\tilde{Q}_2\tilde{Q}_3\tilde{Q}_4$, using an $\mathop{\mathrm{USp}}\nolimits(2n)$ gauge group, followed by an ordinary Seiberg duality for the $\mathop{\mathrm{SU}}\nolimits(2n)$ gauge node.
• Figure 4: Alternative deconfinement for the $\mathop{\mathrm{SU}}\nolimits(2n)$ case in terms of a second $\mathop{\mathrm{SU}}\nolimits(2n)$ gauge node. In this case we do not deconfine the conjugate antisymmetric $\tilde{A}$, but rather the fundamentals and the antifundamental $\tilde{Q}_5$. The next step consists of confining the original $\mathop{\mathrm{SU}}\nolimits(2n)$ gauge node that here has a conjugate antisymmetric, $4$ fundamentals and $2n$ antifundamentals. The final quiver, represented on the right of the figure, can be further reduced, once the baryonic deformations are added, because these deformations trigger a partial Higgs flow, breaking $\mathop{\mathrm{SU}}\nolimits(2n)$ to a symplectic gauge node as explained in the text.
• Figure 5: Deconfinement and sequential duality steps for $\mathop{\mathrm{SU}}\nolimits(2n)$ with one conjugate antisymmetric, $2n+1$ fundamentals, $5$ antifundamentals, reproducing the results of Terning:1997jj without introducing fictitious symmetries.