Vector mesons on the wall

A domain-wall configuration of the $\eta'$ meson bounded by a string (called pancake or Hall droplet) is recently proposed to describe baryons with spin $N_c/2$. In order understand its baryon number as well flavor quantum number, we argue that vector mesons (the $\rho$ and $\omega$ mesons) should play an essential role for consistency whole picture. We determine effective theory large-$N_c$ QCD $N_f$ massless fermions taking into account mixed anomaly involving $\theta$-periodicity global symmetry. The matching requires presence dynamical domain wall on which $U(N_f)_{-N_c}$ Chern-Simons supported. consider boundary conditions be imposed edge wall, conclude there term couples gauge field mesons. discuss impact physics chiral phase transition relation "duality" QCD.