Baryon Construction with $\eta^\prime$ Meson Field

TL;DR

This paper explores the construction of one-flavor baryons as quantum Hall droplets on the $ta'$ domain wall, revealing their topological and fractional charge properties, and discusses implications for baryon confinement and structure.

Contribution

It proposes a novel interpretation of one-flavor baryons as quantum Hall droplets on the $ta'$ domain wall using an effective Chern--Simons--Higgs theory, linking topological solitons to baryon properties.

Findings

Baryons as vortex solutions with spin $N_c/2$

Quarks carry fractional topological charge $1/N_c$

Confinement related to monopoles within the chiral bag

Abstract

In the low-energy regime, baryons with $N_f \geq 2$ have long been constructed as skyrmions or through bag models, but such constructions for $N_f = 1$ are hindered by the trivial topological structure of the meson field. Recent proposals suggest that one-flavor baryons can instead be interpreted as quantum Hall droplets on the $\eta'$ domain wall, providing a potential link to quark--hadron continuity at high density. In retrospect, the qualitative or semi-qualitative construction of one-flavor baryons on the $\eta'$ domain wall reveals that these baryons can be described as quantum Hall droplets, resembling topological solitons akin to skyrmions. Using an effective theory on the $\eta'$ domain wall, which is conjectured to be the Chern--Simons--Higgs theory, it is discussed that its vortex solution with unit baryon numbers naturally has a spin of $N_c/2$, and thus can be interpreted as a baryon or multi-baryon structure. The particle--vortex duality suggests that quarks carry a fractional topological charge of $1/N_c$ and obey fractional statistics. In terms of chiral bag models, confinement can be attributed to the monopoles confined within the bag, and the vector meson fields on the bag surface are essential for ensuring the correct baryon number in the chiral bag framework, thereby providing deeper insights into baryons as non-trivial topological structures of the meson field. In this paper, we review the progress in this development, with a special focus on the $\eta^\prime$ domain wall dynamics. Naive extensions to $N_f \geq 2$ are also discussed.