Domain walls and the CP anomaly in softly broken supersymmetric QCD

In ordinary QCD with light, degenerate, fundamental flavors, CP symmetry is spontaneously broken at θ=π, and domain wall solutions connecting the vacua can be constructed in chiral perturbation theory. In some cases the breaking of CP saturates a 't Hooft anomaly, and anomaly inflow requires nontrivial massless excitations on the domain walls. Analogously, CP can be spontaneously broken in supersymmetric QCD (SQCD) with light flavors and small soft breaking parameters. We study CP breaking and domain walls in softly broken SQCD with Nf<N flavors. Relative to ordinary QCD, the supersymmetric case contains an extra light field, the η′, which has interesting effects on the structure of the walls. Vanishing of the CP anomaly is associated with the existence of multiple domain wall trajectories through field space, including walls which support no nontrivial massless excitations. In cases with an anomaly such walls are forbidden, and their absence in the relevant SQCD theories can be seen directly from the geometry of the low energy field space. In the case Nf=N-1, multiple approximately Bogomol'nyi-Prasad-Sommerfield walls connect the vacua. Corrections to their tensions can be computed at leading order in the soft breaking parameters, producing a phase diagram for the stable wall trajectory. We also comment on domain walls in the similar case of QCD with an adjoint and fundamental flavors, and on the impact of adding an axion in this theory.