Abstract
We study BPS domain walls in four-dimensional N=1N=1 massive SQCD with gauge group SU(N)SU(N) and F<NF<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<NF<N massive SQCD. A similar picture holds also for SQCD with gauge group Sp(N)Sp(N) and F < N+1F<N+1 flavors.
Highlights
Introduction and summary of resultsInteresting progress has been recently made in understanding the dynamics of quantum field theories (QFTs) in three space-time dimensions
For m < 0, that corresponds to small 4d mass m4d compared to the SQCD scale Λ, there are multiple vacua in which the low-energy effective theory is the product of a topological quantum field theory (TQFT) and a supersymmetric nonlinear sigma model
With quartic superpotential on both sides
Summary
Interesting progress has been recently made in understanding the dynamics of quantum field theories (QFTs) in three space-time dimensions. For m < 0, that corresponds to small 4d mass m4d compared to the SQCD scale Λ, there are multiple vacua in which the low-energy effective theory is the product of a TQFT and a supersymmetric nonlinear sigma model. The new idea is to construct “hybrid” walls, combining standard domain walls of the Wess-Zumino type on the mesonic space with sharp transitions in an unbroken SYM sector that is present on the mesonic space This construction exactly matches the intricate vacuum structure displayed by theory (1.1) at m < 0. This analysis will already encode several nontrivial checks.
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