Skyrmions and Fractional Quantum Hall Droplets Unified by Hidden Symmetries in Dense Matter

A chain of connections in compressed baryonic matter, up-to-date glaringly missing in nuclear effective field theory, between intrinsic or emergent symmetries of QCD, mesons-gluons dualities, vector meson dominance and Chern-Simons fields has recently been revealed, presaging a possible new paradigm in nuclear theory. It indicates a ubiquitous role, thus far unexplored, of hidden symmetries -- flavor-local and scale -- permeating from dilute baryonic systems to normal nuclear matter and then to compact-star matter. Here I give a brief account of the possibly "indispensable" relevance of the $\eta^\prime$ singular ring, a.k.a. fractional quantum Hall (FQH) droplet, to the properties of the lowest-lying vector mesons $\omega$ and $\rho$, relevant to dilepton production processes, argued to be Seiberg-dual to the gluons near the chiral restoration.