3D dualities and supersymmetry enhancement from domain walls

Abstract

We test recently proposed IR dualities and supersymmetry enhancement by studying the supersymmetry on domain walls. In the SU (3) Wess-Zumino model studied in [1,2], we show that domain walls exhibit supersymmetry enhancement. This model was conjectured to be dual to an N = 2 abelian gauge theory. We show that domain walls on the gauge theory side are consistent with the proposed duality, as they are described by the same effective theory on the wall. In [3], a third model was conjectured to be dual to the same IR theory. We study the phases and domain walls of this model and we show that they also agree. We then consider the analogous SU (5) Wess-Zumino model, and study its mass deformations and phases. We argue that even though one might expect supersymmetry enhancement in this model as well, the analysis of its domain walls shows that there is none. Finally, we study the N = 2 model in [4] which was conjectured to have N = 4 supersymmetry in the IR. In this case we don't see the supersymmetry enhancement on the domain wall; however, we argue that half-BPS domain walls of the N = 2 algebra are quarter-BPS of the N = 4 algebra. This is then in agreement with the conjectured enhancement, even though it does not show that it takes place.

The bi-fundamental gauge theory in 3+1 dimensions: the vacuum structure and a cascade

“…(Note again that the phase diagram allows for several inequivalent types of domain walls.) Similar questions were recently studied in other examples, see for instance [14][15][16][17][18][19][20][21][22].…”

Global aspects of spaces of vacua

“…We start by matching vacuum crossing across four theories which are conjectured to be dual. Consider the theory described in [14,15] and further analyzed in [16]. This is a 3d N = 1 WZ model with a superfield Φ which is a traceless Hermitian 3 × 3 matrix.…”

“…Just like the 3d model, there are signs that this CFT has emergent N = 2 SUSY. Specifically, one can repeat the analysis of [16] for the 2d theory. The calculation is almost identical to the 3d case, and the result is that the domain walls between the two gapped vacua have emergent SUSY with 2 supercharges.…”

“…Once again we can solve for the vacua of the theory as a function of the masses. The vacua were found in [16], where it was found that vacua exist only when the adjoint scalar s in the vector multiplet takes the form s = diag(σ, σ, −2σ). Apart from some rays emanating from the origin, there are exactly two solutions for the vacuum, with σ taking two of the possible values σ ∈ {0, m 1 , m 2 , m 3 }.…”

Domain walls in 4d $$ \mathcal{N} $$ = 1 SYM

“…For a partial list of references on domain walls in 4d gauge theories see e.g. [10][11][12][13][14][15][16][17][18][19][20][21].…”