Abstract
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.
Highlights
On a domain wall separating two vacua is an SU(Nc)1 Chern-Simons (CS) theory.1 One can consider the ’t Hooft anomaly for symmetries in the parameter space of the theory [16, 17]
We find that the anomalous coupling between η and the background fields implies that the global U(1) symmetry of the CS theory is identified with the baryon symmetry, and the exited states with a unit U(1) charge belong to the correct representation of the flavor symmetry
We argue that the CS theory, not CS Higgs theory, is required by the matching of the anomaly while the vector mesons mix with the gauge field of the CS theory on the edge of the pancake
Summary
Before going into the technical detail, we start with a physical question in QCD where the baryon number symmetry, U(1)B, is weakly gauged. Where AB is the baryon gauge field where it is normalized such that the baryon has the charge unity. This term induces the Witten effect2 [36] when η changes from 0 to 2π. When we go back to QCD, the monopole with the unit magnetic charge is allowed by the Dirac quantization condition. The effective theory should allow such a monopole to exist. Once it is allowed, since there is no gluon degrees of freedom in the effective theory, one cannot attach the color magnetic flux anymore, and the Dirac quantization condition seems to be just violated. We will see that QCD choose the latter by having a CS theory on the wall
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