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

Abstract

We analyze the moduli space dynamics of domain walls in $SU(N)$ QCD at $\bar{\theta }=\pi$, by softly breaking $\mathcal{N}=1$ 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.

8 pages, 1 figure. V2: References added; Version published in Phys. Rev. D