Vector mesons on the wall

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