{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:40:48Z","timestamp":1760031648883,"version":"build-2065373602"},"reference-count":136,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of China (NSFC)","award":["12347103","2021YFC2202900","ZXL2024363"],"award-info":[{"award-number":["12347103","2021YFC2202900","ZXL2024363"]}]},{"name":"National Key R&amp;D Program of China","award":["12347103","2021YFC2202900","ZXL2024363"],"award-info":[{"award-number":["12347103","2021YFC2202900","ZXL2024363"]}]},{"name":"Gusu Talent Innovation Program","award":["12347103","2021YFC2202900","ZXL2024363"],"award-info":[{"award-number":["12347103","2021YFC2202900","ZXL2024363"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the low-energy regime, baryons with Nf\u22652 have long been constructed as skyrmions or through bag models, but such constructions for Nf=1 are hindered by the trivial topological structure of the meson field. Recent proposals suggest that one-flavor baryons can instead be interpreted as quantum Hall droplets on the \u03b7\u2032 domain wall, providing a potential link to quark\u2013hadron continuity at high density. In retrospect, the qualitative or semi-qualitative construction of one-flavor baryons on the \u03b7\u2032 domain wall reveals that these baryons can be described as quantum Hall droplets, resembling topological solitons akin to skyrmions. Using an effective theory on the \u03b7\u2032 domain wall, which is conjectured to be the Chern\u2013Simons\u2013Higgs theory, it is discussed that its vortex solution with unit baryon numbers naturally has a spin of Nc\/2, and thus can be interpreted as a baryon or multi-baryon structure. The particle\u2013vortex duality suggests that quarks carry a fractional topological charge of 1\/Nc and obey fractional statistics. In terms of chiral bag models, confinement can be attributed to the monopoles confined within the bag, and the vector meson fields on the bag surface are essential for ensuring the correct baryon number in the chiral bag framework, thereby providing deeper insights into baryons as non-trivial topological structures of the meson field. In this paper, we review the progress in this development, with a special focus on the \u03b7\u2032 domain wall dynamics. Naive extensions to Nf\u22652 are also discussed.<\/jats:p>","DOI":"10.3390\/sym17040477","type":"journal-article","created":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T11:06:48Z","timestamp":1742555208000},"page":"477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Baryon Construction with \u03b7\u2032 Meson Field"],"prefix":"10.3390","volume":"17","author":[{"given":"Fan","family":"Lin","sequence":"first","affiliation":[{"name":"School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China"},{"name":"Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Yong-Liang","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Frontier Sciences, Nanjing University, Suzhou 215163, China"},{"name":"International Center for Theoretical Physics Asia-Pacific (ICTP-AP), UCAS, Beijing 100190, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1343","DOI":"10.1103\/PhysRevLett.30.1343","article-title":"Ultraviolet Behavior of Nonabelian Gauge Theories","volume":"30","author":"Gross","year":"1973","journal-title":"Phys. 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