Probing Fractional Quantum Hall Sheets in Dense Baryonic Matter

TL;DR

This paper explores the theoretical description of baryons as fractional quantum Hall droplets in dense nuclear matter, incorporating symmetries and anomalies to understand their behavior in extreme astrophysical environments.

Contribution

It introduces a novel approach to modeling baryons as quantum Hall droplets using nuclear scale-chiral effective field theory with $U_A(1)$ anomaly considerations.

Findings

Baryons can be described as fractional quantum Hall droplets involving Chern-Simons fields.

The approach suggests the existence of single-flavor baryons in superdense matter, possibly in quark stars.

Implications for baryon-quark continuity and phase transitions in dense matter.

Abstract

Unlike the octet baryons for $N_f=3$, there is no skyrmion coming from the $\eta^\prime$ meson. It is instead described as a fractional quantum Hall droplet, a pancake or a pita involving a singular $\eta^\prime$ ring in which Chern-Simons fields live. By incorporating hidden local symmetry and hidden scale symmetry in nuclear dynamics, I describe how to access baryon-charged quantum Hall droplets in dense nuclear matter in terms of the nuclear scale-chiral effective field theory approach ``G$n$EFT" with the $U_A(1)$ anomaly taken into account. I discuss how the single-flavor baryon that I will call ${\cal B}^s$ could be exposed in superdense baryonic matter, figuring, perhaps, in ``quark stars" associated with the baryon-quark continuity involving CFL or phase transitions.