Mapping topology of skyrmions and fractional quantum Hall droplets to nuclear EFT for ultra-dense baryonic matter

TL;DR

This paper maps the topological structures of baryonic matter, including skyrmions and fractional quantum Hall droplets, to a nuclear effective field theory with hidden symmetries, providing insights into ultra-dense matter and compact stars.

Contribution

It introduces a unified framework connecting skyrmion and FQH droplet topologies to hidden symmetries in nuclear EFT, relevant for ultra-dense baryonic matter.

Findings

Consistent with observations in nuclear and compact-star matter.

Unifies skyrmion and FQH droplet topologies via hidden local symmetry.

Explores role of FQH droplets near scale-chiral restoration.

Abstract

We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory so constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are "local flavor symmetry" of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden "quantum scale symmetry" with an IR fixed point with a "genuine dilaton (GD)" characterized by non-vanishing pion and dilaton decay constants. Both the skyrmion topology for $N_f \geq 2$ baryons and the fractional quantum Hall (FQH) droplet topology for $N_f=1$ baryons are unified in the "homogeneous/hidden" Wess-Zumino term in the hidden local symmetry (HLS) Lagrangian. The possible indispensable role of the FQH droplets in going beyond the density regime of compact stars approaching scale-chiral restoration is explored by moving toward the limit where both the dilaton and the pion go massless.