Living on the walls of super-QCD

We study BPS domain walls in four-dimensional N = 1 massive SQCD with gauge group SU (N) and F < N flavors. We propose a class of three-dimensional Chern-Simons-matter theories to describe the effective dynamics on the walls. Our proposal passes several checks, including the exact matching between its vacua and the solutions to the four-dimensional BPS domain wall equations, that we solve in the small mass regime. As the flavor mass is varied, domain walls undergo a second-order phase transition, where multiple vacua coalesce into a single one. For special values of the parameters, the phase transition exhibits supersymmetry enhancement. Our proposal includes and extends previous results in the literature, providing a complete picture of BPS domain walls for F < N massive SQCD. A similar picture holds also for SQCD with gauge group Sp (N) and F < N + 1 flavors.