000013612 001__ 13612 000013612 005__ 20241002042305.0 000013612 02470 $$ahttps://doi.org/10.1103/PhysRevD.110.085003$$2doi 000013612 037__ $$aTEXTUAL 000013612 037__ $$bArticle 000013612 041__ $$aeng 000013612 245__ $$aImpossible symmetries and conformal gravity 000013612 269__ $$a2024-10-01 000013612 336__ $$aArticle 000013612 520__ $$aWe explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetries arising from these currents. In some cases, the anomaly cannot be reproduced by any local and unitary theory, indicating that the corresponding symmetries are impossible, in the sense that they cannot appear in a Lorentzian physical system. We give a general construction and illustrate it with several examples. Most notably, we study conformal gravity from this perspective, describing the higher-form symmetries of the linear theory and showing how it can be understood in terms of anomalies. Along the way we clarify some aspects of electric-magnetic duality in linear conformal gravity. 000013612 536__ $$oU.S. Department of Energy$$cDE-SC0009946 000013612 536__ $$oU.S. Department of Energy$$cDE-SC0009924 000013612 536__ $$oSimons Foundation$$c488649 000013612 536__ $$oSwiss National Science Foundation$$c200020 197160 000013612 536__ $$oNational Centre of Competence in Research SwissMAP 000013612 536__ $$oNational Science Foundation$$cPHY-1748958 000013612 536__ $$oNational Science Foundation$$cPHY-2210452 000013612 540__ $$a<p> Published by the American Physical Society under the terms of the <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International license.</a></p> 000013612 542__ $$fCC BY 000013612 690__ $$aBiological Sciences Division 000013612 691__ $$aAstronomy and Astrophysics 000013612 692__ $$aKavli Institute for Cosmological Physics 000013612 7001_ $$aHinterbichler, Kurt$$uCase Western Reserve University 000013612 7001_ $$1https://orcid.org/0000-0002-6432-5272$$2ORCID$$aJoyce, Austin$$uUniversity of Chicago 000013612 7001_ $$aMathys, Grégoire$$uEcole Polytechnique Fédérale de Lausanne 000013612 773__ $$tPhysical Review D 000013612 8564_ $$9f7e7436c-0b23-4a40-823a-42297ce4d4a6$$ePublic$$s1426582$$uhttps://knowledge.uchicago.edu/record/13612/files/PhysRevD.110.085003.pdf 000013612 908__ $$aI agree 000013612 909CO $$ooai:uchicago.tind.io:13612$$pGLOBAL_SET 000013612 983__ $$aArticle