Domain wall moduli in softly-broken SQCD at $\barθ=π$

TL;DR

The paper investigates domain walls in SU($N$) QCD at $\bar{\theta}=\pi$ by connecting BPS walls in softly broken ${\cal N}=1$ SQCD with $N_f=N$ to their worldvolume moduli. It shows that neighbouring walls harbor flavour moduli forming a $\mathbb{C}P^{N-1}$ sigma model, and in the ${\rm SU}(2)$, $N_f=2$ case, a bulk Wess-Zumino term induces a parity-violating Hopf term on the wall with coefficient $\Theta_H=\pi$. Soft SUSY breaking via a diagonal $F$-term preserves the flavour symmetry and leaves these walls and their moduli intact at $\bar{\theta}=\pi$, providing a concrete bridge to QCD-like dynamics. The analysis extends to general ${\rm SU}(N)$ where the 1-wall moduli remain $\mathbb{C}P^{N-1}$ and acquire a wall Hopf term, highlighting a topological structure in the domain-wall sector with potential implications for non-supersymmetric QCD and future extensions.

Abstract

We analyze the moduli space dynamics of domain walls in $SU(N)$ QCD at $\barθ=π$, 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 $\barθ=π$ so that there are two degenerate vacua.

Figures (1)

• Figure 1: A schematic representation of the perturbation to the $N$ degenerate vacua of SQCD (for $N=5$), which creates a potential tilting the plane, and for $\bar{\theta}=\pi$ results in two degenerate vacua which allow for interpolating domain walls.