{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:32:13Z","timestamp":1760149933402,"version":"build-2065373602"},"reference-count":61,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T00:00:00Z","timestamp":1695600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFC2203003","12247101"],"award-info":[{"award-number":["2021YFC2203003","12247101"]}]},{"name":"National Natural Science Foundation of China","award":["2021YFC2203003","12247101"],"award-info":[{"award-number":["2021YFC2203003","12247101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates gauge invariance in a bulk massless q-form field on a p-brane with codimension two, utilizing a general Kaluza\u2013Klein (KK) decomposition. The KK decomposition analysis reveals four distinct KK modes: the conventional q-form, two (q\u22121)-forms and one (q\u22122)-form. These diverse modes are essential for maintaining gauge invariance. We also find eight Schr\u00f6dinger-like equations for the four modes due to the two extra dimensions, and their mass spectra are closely related. The KK decomposition process gives rise to four dualities on the p-brane, originating from the inherent Hodge duality present in the bulk. Notably, these dual symmetries play a significant role in maintaining the equivalence of bulk dual fields during dimensional reduction.<\/jats:p>","DOI":"10.3390\/sym15101819","type":"journal-article","created":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T03:53:00Z","timestamp":1695700380000},"page":"1819","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Q-Form Field on a p-Brane with Codimension Two"],"prefix":"10.3390","volume":"15","author":[{"given":"Ziqi","family":"Chen","sequence":"first","affiliation":[{"name":"Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"},{"name":"Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou 730000, China"},{"name":"Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chun\u2019e","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"},{"name":"Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou 730000, China"},{"name":"Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Yang","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"},{"name":"Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou 730000, China"},{"name":"Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Zhao","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"},{"name":"Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou University, Lanzhou 730000, China"},{"name":"Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1088\/1475-7516\/2012\/02\/031","article-title":"Cosmological dynamics of brane f(R) gravity","volume":"1202","author":"Haghani","year":"2012","journal-title":"JCAP"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1088\/1126-6708\/2009\/02\/035","article-title":"Domain-wall brane models of an infinite extra dimension","volume":"902","author":"George","year":"2009","journal-title":"JHEP"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"046008","DOI":"10.1103\/PhysRevD.62.046008","article-title":"Modeling the fifth-dimension with scalars and gravity","volume":"62","author":"DeWolfe","year":"2000","journal-title":"Phys. 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