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Phys."],"published-print":{"date-parts":[[2019,10]]},"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n          <\/jats:title>\n          <jats:p>We study the categorical generalizations of a <jats:italic>BF<\/jats:italic> theory to 2<jats:italic>BF<\/jats:italic> and 3<jats:italic>BF<\/jats:italic> theories, corresponding to 2-groups and 3-groups, in the framework of higher gauge theory. In particular, we construct the constrained 3<jats:italic>BF<\/jats:italic> actions describing the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. The action is naturally split into a topological sector and a sector with simplicity constraints, adapted to the spinfoam quantization programme. In addition, the structure of the 3-group gives rise to a novel gauge group which specifies the spectrum of matter fields present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. This allows us to rewrite the whole Standard Model coupled to gravity as a constrained 3<jats:italic>BF<\/jats:italic> action, facilitating the nonperturbative quantization of both gravity and matter fields. Moreover, the presence and the properties of this new gauge group open up a possibility of a nontrivial unification of all fields and a possible explanation of fermion families and all other structure in the matter spectrum of the theory.<\/jats:p>","DOI":"10.1007\/jhep10(2019)222","type":"journal-article","created":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T17:17:49Z","timestamp":1571851069000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Higher gauge theories based on 3-groups"],"prefix":"10.1007","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2310-5281","authenticated-orcid":false,"given":"T.","family":"Radenkovi\u0107","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6977-4870","authenticated-orcid":false,"given":"M.","family":"Vojinovi\u0107","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,10,22]]},"reference":[{"key":"11644_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755804","volume-title":"Quantum gravity","author":"C Rovelli","year":"2004","unstructured":"C. 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