{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T08:33:00Z","timestamp":1777710780549,"version":"3.51.4"},"reference-count":231,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T00:00:00Z","timestamp":1658188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Center for Mathematical Sciences and Applications at Harvard University","award":["DMS-1607871"],"award-info":[{"award-number":["DMS-1607871"]}]},{"name":"startup fund at UCSD","award":["DMS-1607871"],"award-info":[{"award-number":["DMS-1607871"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The most well-known mechanism for fermions to acquire a mass is the Nambu\u2013Goldstone\u2013Anderson\u2013Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator\/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG.<\/jats:p>","DOI":"10.3390\/sym14071475","type":"journal-article","created":{"date-parts":[[2022,7,19]],"date-time":"2022-07-19T08:28:25Z","timestamp":1658219305000},"page":"1475","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":63,"title":["Symmetric Mass Generation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9396-9010","authenticated-orcid":false,"given":"Juven","family":"Wang","sequence":"first","affiliation":[{"name":"Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4080-5340","authenticated-orcid":false,"given":"Yi-Zhuang","family":"You","sequence":"additional","affiliation":[{"name":"Department of Physics, University of California, San Diego, CA 92093, USA"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2848","DOI":"10.1103\/PhysRevD.21.2848","article-title":"Path integral for gauge theories with fermions","volume":"21","author":"Fujikawa","year":"1980","journal-title":"Phys. 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