Mildly flavoring domain walls in Sp(N) SQCD

We consider supersymmetric domain walls of four-dimensional 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 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 N=1 gauge theories.

Automated summary

In the study of supersymmetric domain walls in four-dimensional N = 1 Sp(N) SQCD with F = N + 1 and F = N + 2 flavors, numerical methods are used to examine the differential equations defining the walls and the 3d N = 1 Chern-Simons-matter theories that describe the effective dynamics on the walls. While various tests are passed, including dualities and matching of the vacua, the semiclassical analysis of vacua for F = N + 2 suggests the presence of strong coupling phenomena yet to be understood in the 3d N = 1 gauge theories.