Vector mesons on the wall

TL;DR

This paper explores the role of vector mesons in a domain-wall configuration of the $ ext{eta'}$ meson, linking anomaly matching, effective theories, and baryon quantum numbers in large-$N_c$ QCD.

Contribution

It introduces a boundary term coupling vector mesons to a Chern-Simons theory on a domain wall, providing a novel perspective on baryon structure and anomaly matching in QCD.

Findings

Vector mesons are essential for the consistency of baryon descriptions.

A boundary term couples vector mesons to the Chern-Simons theory on the domain wall.

Implications for chiral phase transition and QCD duality are discussed.

Abstract

A domain-wall configuration of the $\eta'$ meson bounded by a string (called a pancake or a Hall droplet) is recently proposed to describe the baryons with spin $N_c/2$. In order to understand its baryon number as well as the flavor quantum number, we argue that the vector mesons (the $\rho$ and $\omega$ mesons) should play an essential role for the consistency of the whole picture. We determine the effective theory of large-$N_c$ QCD with $N_f$ massless fermions by taking into account a mixed anomaly involving the $\theta$-periodicity and the global symmetry. The anomaly matching requires the presence of a dynamical domain wall on which a $U(N_f)_{-N_c}$ 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 $U(N_f)_{-N_c}$ 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.