Phases of $$ \mathcal{N} $$ = 1 quivers in 2 + 1 dimensions

Abstract

We consider the IR phases of two-node quiver theories with $$ \mathcal{N} $$ N = 1 supersymmetry in d = 2 + 1 dimensions. It turns out that the discussion splits into two main cases, depending on whether the Chern-Simons levels associated with the two nodes have the same sign, or the opposite signs, with the latter case being more non-trivial. The determination of the phase diagrams allows us to conjecture certain infrared dualities involving either two quiver theories, or a quiver and adjoint QCD. We also provide a short discussion on quivers possessing time reversal symmetry.

Monopoles and confinement in three dimensions from holography

“…Furthermore, localization techniques cannot be applied, so N = 1 theories are almost on par with non-supersymmetric models concerning the analysis of their non-perturbative properties. Although there has been some work studying the vacuum structure of N = 1 theories [14,15], as far as we are aware non-Abelian quiver theories with vanishing Chern-Simons levels like the ones considered here have not been studied before. In this regard, our analysis might also shed further light on the phase structure of N = 1 theories.…”

“…Another interesting direction would be to study the phase diagram of a mirror dual [34,35], in the particle-vortex dual sense [36]. For the amount of supersymmetry we are considering, mirror duality of N = 1 QED was studied in [37], and there are generalizations for the Abelian theory of probe D2-branes on cones with special holonomy [38,39], and for non-Abelian theories with Chern-Simons terms [15], but there does not seem to be an extension to the non-Abelian case for vanishing Chern-Simons levels. In our case the expectation is that in the mirror dual the monopole magnetic field would translate into a baryon charge density [40], thus allowing to explore "nuclear matter" in a holographic setup without having to introduce additional flavor D-branes or instantons on those.…”