Mildly Flavoring Domain Walls in Sp(N) SQCD

TL;DR

This paper investigates supersymmetric domain walls in Sp(N) SQCD with specific flavors, analyzing their solutions and effective 3d theories, revealing complex phenomena and partial successes in understanding their dynamics.

Contribution

It provides a numerical classification of domain wall solutions and proposes effective 3d theories, highlighting new insights and challenges in the strong coupling regime.

Findings

Numerical solutions classify domain walls for F=N+1 and F=N+2.

Special case of parity-invariant walls requires infinitesimal deformations for complete solutions.

Effective 3d theories match vacua and dualities, but face partial semiclassical analysis success for F=N+2.

Abstract

We consider supersymmetric domain walls of four-dimensional $\mathcal{N}\!=\!1$ $Sp(N)$ SQCD with $F\!=\!N+1$ and $F\!=\!N+2$ flavors. First, we study numerically the differential equations defining the walls, classifying the solutions. When $F\!=\!N+2$, in the special case of the parity-invariant walls, the naive analysis does not provide all the expected solutions. We show that an infinitesimal deformation of the differential equations sheds some light on this issue. Second, we discuss the $3d$ $\mathcal{N}\!=\!1$ Chern-Simons-matter theories that should describe the effective dynamics on the walls. These proposals pass various tests, including dualities and matching of the vacua of the massive $3d$ theory with the $4d$ analysis. However, for $F\!=\!N+2$, the semiclassical analysis of the vacua is only partially successful, suggesting that yet-to-be-understood strong coupling phenomena are into play in our $3d$ $\mathcal{N}\!=\!1$ gauge theories.