Skyrmions, Quantum Hall Droplets, and one current to rule them all

Understand

We introduce a novel Skyrme-like conserved current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry.

• The associated charge is equivalent to the skyrmion charge for any smooth configuration.
• In addition, there exist singular configurations that can be identified as N_f=1 baryons charged under the new symmetry.
• Under this identification, the vector mesons play the role of the Chern-Simons vector fields living on the quantum Hall droplet that forms the N_f=1 baryon.