Confined Monopoles in Chiral Bag

The chiral bag model offers a dual description of hadron physics in terms of quarks and hadrons in the sense of Cheshire Cat principle. In this work, we find that, within the chiral bag, confinement is likely caused by monopole condensation. The chiral bag surface can be interpreted as an $η'$ domain wall, where a dynamical Chern-Simons theory emerges. Under level-rank duality, the Chern-Simons theory serves as the counterterm introduced to block the so-called color charge leakage. To ensure the correct net baryon number of the full chiral bag, an additional Chern-Simons theory involving the vector meson field arises on the bag surface and extends outside the bag. This leads to a Chern-Simons-Higgs theory localized on the $η'$ domain wall, as previously conjectured. We also propose that the skyrmion description of baryons could be understood as a system of monopoles enveloped by a meson cloud.