{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T04:31:56Z","timestamp":1784003516273,"version":"3.55.0"},"reference-count":60,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T00:00:00Z","timestamp":1627257600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analyzed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane.<\/jats:p>","DOI":"10.3390\/sym13081345","type":"journal-article","created":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T04:19:30Z","timestamp":1627273170000},"page":"1345","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["First-Order Formalism and Thick Branes in Mimetic Gravity"],"prefix":"10.3390","volume":"13","author":[{"given":"Qun-Ying","family":"Xie","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"},{"name":"Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi-Ming","family":"Fu","sequence":"additional","affiliation":[{"name":"Institute of Physics, Shaanxi University of Technology, Hanzhong 723000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tao-Tao","family":"Sui","sequence":"additional","affiliation":[{"name":"Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Zhao","sequence":"additional","affiliation":[{"name":"Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Zhong","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Hunan University, Changsha 410082, China"},{"name":"Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University, Changsha 410082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/JHEP11(2013)135","article-title":"Mimetic Dark Matter","volume":"2013","author":"Chamseddine","year":"2013","journal-title":"J. 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