A - BCD dualities

TL;DR

This work builds a comprehensive framework of 4d and 3d IR dualities relating SU$(N)$ gauge theories with an antisymmetric tensor and four fundamentals to USp$(2M)$ and SO-based theories with two-index tensors. It establishes a 4d self-duality for SU$(4)$ via tensor deconfinement and Seiberg-like dualities, then analyzes baryonic deformations that trigger RG flows to novel SU$-$USp and SU$-$SO dual pairs, supported by superconformal index matching. The 3d reductions follow the ARSW prescription, yielding rich SU/USp and SU/SO dualities with monopole superpotentials, which are further illuminated by the duplication formula for hyperbolic Gamma functions. Tensor deconfinement provides independent proofs of these dualities, and the work also explores phase structure, conformal windows, and potential 4d parent theories for several 3d confining dualities. The results deepen the understanding of duality webs across dimensions and offer precise computational checks via partition functions and indices, with implications for broader classes of tensor-based gauge theories.

Abstract

In this paper we propose 4d and 3d dualities among special unitary gauge theories with fundamentals and antisymmetric flavors and symplectic or orthogonal gauge theories with fundamentals and two index tensor matter. The various dualities originate from a conjectured 4d self-duality for $SU(N)$ with an antisymmetric and four fundamental flavors. While we provide a proof of such self duality for $SU(4)$, we focus on baryonic deformations for the cases at higher ranks. The deformations give rise to RG flows, deforming the self duality into new types of dualities, involving $SU(N)$ and $USp(2M)$ gauge theories, where the precise value of $M$ depends on the baryonic deformation. We provide strong checks on the validity of these dualities, by proving the integral identities among their superconformal index. By dimensional reduction on a circle, real mass flows and other deformations we then find a rich set of new dualities in 3d. These dualities are first conjectured from localization, by the application of the duplication formula for the one loop determinants of the matter fields, and then they are proved by using the tensor deconfinement technique.

Figures (13)

• Figure 1: In this figure we have plot the various steps of tensor deconfinements and ordinary dualities used to derive the $\mathrm{SU}(4)$ (self-)dual model with superpotential $W_D$.
• Figure 2: Quiver obtained by deconfining the two antisymmetric of $\mathrm{SU}(4)$ (red node) in terms of two $\mathrm{SU}(2)$ gauge groups (blue nodes).
• Figure 3: First deconfinement sequence for $\mathrm{SU}(N)_1$ gauge theory with 4 fundamental flavors, 1 antisymmetric flavor and vanishing superpotential. The case $N=2n$ has been studied in subsection \ref{['subsec2n']} while the case of $N=2n+1$ has been studied in subsection \ref{['subsec2np1']}.
• Figure 9: Schematic description of the derivation of the SU/USp duality for the 3d $SU(2n)$ model with an antisymmetric pair, four fundamentals and two antifundamentals, through tensor deconfinement and elementary dualities.
• Figure 10: Scheme of the proof of the duality between $\mathrm{SU}(2n)$ with a symmetric and a conjugate antisymmetric and $\mathrm{USp}(2n-2)$ with an adjoint. In the first quiver we represent the field content of the electric gauge theory. In the second figure we represent the charged fields after deconfining the two tensors using an $\mathrm{SO}(2n)$ and an $\mathrm{USp}(2n-2)$ gauge group. The first quiver is obtained after confining the original $\mathrm{SU}(2n)$ gauge group. The final quiver is obtained by confining the $\mathrm{SO}(2n)$ gauge group and it corresponds to the expected dual model studied from the duplication formula at the level of the three sphere partition function.