Domain wall moduli in softly-broken SQCD at $\bar\theta=\pi$

TL;DR

This paper studies the dynamics of domain walls in softly-broken SQCD at =, revealing that certain moduli-space features persist under soft supersymmetry breaking, with implications for understanding non-perturbative effects.

Contribution

It demonstrates that the moduli space of domain walls in softly-broken SQCD retains key features, including a  sigma model with a Hopf term, at =.

Findings

The  sigma model on domain walls includes a Hopf term with quantized coefficient.

Moduli-space dynamics survive soft supersymmetry breaking at =, maintaining degenerate vacua.

The analysis applies explicitly to the SU(2) gauge group with two flavors.

Abstract

We analyze the moduli space dynamics of domain walls in $SU(N)$ QCD at $\bar\theta=\pi$, by softly breaking ${\cal N}\! =\!1$ SQCD with sfermion mixing. In the supersymmetric limit, BPS domain walls between neighbouring vacua are known to possess non-translational flavour moduli that form a $\mathcal{C} P^{N-1}$ sigma model. For the simplest case with gauge group $SU(2)$ and $N_f=2$, we show that this sigma model also exhibits a Hopf term descending from the bulk Wess-Zumino term with a quantized coefficient. On soft-breaking of supersymmetry via sfermion mixing that preserves the flavour symmetry, these walls and their moduli-space dynamics survives when $\bar\theta=\pi$ so that there are two degenerate vacua.