Vector mesons on the wall

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 $$ \mathrm{U}{\left({N}_f\right)}_{-{N}_c} $$ 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 $$ \mathrm{U}{\left({N}_f\right)}_{-{N}_c} $$ 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.

Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term

“…After the first version of this paper appeared, there appeared a preprint [21] in which the authors claim they disagree with the proposal made in this work. We comment about the differences and similarities between the two proposals in appendix B.…”

“…In this appendix we comment about the proposal made in [21] and the apparent disagreement with our paper. The authors of [21] describe the N f = 1 baryon as a finite η = π pancake with a U(1) N CS theory living on it. The charge of the baryon is given by the winding of the CS vector field along the boundary of the pancake.…”

“…This construction is very similar to the construction of [10,11] and to the one described in this work. The main difference is that we identified this CS field with the ω vector meson, while in [21], the CS field was an emergent U(1) N vector field bounded to the η = π DW. This field is denoted by c. However, we want to argue that even though the two proposals sound very different, there is no clear contradiction between the two.…”

“…These two results rely on a certain value of the hWZ action parameters. In [21], the hWZ action is written with exactly the same parameters. See equations (90-91) of [21].…”

“…In [21], the hWZ action is written with exactly the same parameters. See equations (90-91) of [21]. This automatically implies that they get from the hWZ action the same baryon current and the same CS term for ω on the DW.…”