Domain Walls and the $CP$ Anomaly in Softly Broken Supersymmetric QCD

TL;DR

This paper explores how domain walls and $CP$ symmetry breaking in softly broken supersymmetric QCD relate to anomalies, revealing new structures influenced by the $ extit{ ext{eta}}'$ field and soft breaking parameters.

Contribution

It introduces a detailed analysis of $CP$ breaking and domain wall structures in softly broken SQCD, highlighting the role of the $ extit{ ext{eta}}'$ and anomaly considerations.

Findings

Multiple domain wall trajectories exist when $CP$ anomaly is absent.

Walls supporting no massless excitations are associated with anomaly cancellation.

A phase diagram for stable wall trajectories is derived for $N_f=N-1$.

Abstract

In ordinary QCD with light, degenerate, fundamental flavors, $CP$ symmetry is spontaneously broken at $\theta=\pi$, and domain wall solutions connecting the vacua can be constructed in chiral perturbation theory. In some cases the breaking of $CP$ saturates an 't Hooft anomaly, and anomaly inflow requires nontrivial massless excitations on the domain walls. Analogously, $CP$ can be spontaneously broken in supersymmetric QCD with light flavors and small soft breaking parameters. We study $CP$ breaking and domain walls in softly broken SQCD with $N_f<N$ flavors. Relative to ordinary QCD, the supersymmetric case contains an extra light field, the $\eta^\prime$, 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 $N_f=N-1$, multiple approximately-BPS 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.