{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:11:10Z","timestamp":1760029870898,"version":"build-2065373602"},"reference-count":74,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Origins Excellence Cluster and the German-Israel-Project (DIP) on Holography and the Swampland"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is widely believed that global symmetries must be broken in Quantum Gravity. This includes higher-form symmetries, which are commonplace in supergravity coupled to vector multiplets. Recently, a quantitative criterion for the breaking of (higher-form) symmetries in effective field theories of gravity has been proposed. We studied this criterion in the context of center one-form symmetries broken by BPS states in Calabi\u2013Yau compactifications of type IIA string theory and M-theory. In a simple toy model, we evaluated the parameters quantifying the extent of symmetry breaking for large and small values of the moduli, comparing the scales of significant breaking with other relevant physical scales.<\/jats:p>","DOI":"10.3390\/sym17040490","type":"journal-article","created":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T06:25:15Z","timestamp":1742883915000},"page":"490","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Center Symmetry Breaking in Calabi\u2013Yau Compactifications"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6183-594X","authenticated-orcid":false,"given":"Ivano","family":"Basile","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Physik (Werner-Heisenberg-Institut), Boltzmannstr. 8, 85748 Garching, Germany"},{"name":"Arnold-Sommerfeld Center for Theoretical Physics, Ludwig Maximilian University of Munich, Theresienstra\u00dfe 37, 80333 Munchen, Germany"}]},{"given":"Pouya","family":"Golmohammadi","sequence":"additional","affiliation":[{"name":"Arnold-Sommerfeld Center for Theoretical Physics, Ludwig Maximilian University of Munich, Theresienstra\u00dfe 37, 80333 Munchen, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1007\/JHEP02(2015)172","article-title":"Generalized Global Symmetries","volume":"2","author":"Gaiotto","year":"2015","journal-title":"J. High Energy Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2024.01.007","article-title":"ICTP lectures on (non-)invertible generalized symmetries","volume":"1063","year":"2024","journal-title":"Phys. Rep."},{"key":"ref_3","unstructured":"Brennan, T.D., and Hong, S. (2023). Introduction to Generalized Global Symmetries in QFT and Particle Physics. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2023.11.002","article-title":"Lectures on generalized symmetries","volume":"1051","author":"Bhardwaj","year":"2024","journal-title":"Phys. Rep."},{"key":"ref_5","unstructured":"Shao, S.H. (2023). What\u2019s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"161601","DOI":"10.1103\/PhysRevLett.129.161601","article-title":"Noninvertible Global Symmetries in the Standard Model","volume":"129","author":"Choi","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"125028","DOI":"10.1103\/PhysRevD.110.125028","article-title":"Categorical symmetry of the standard model from gravitational anomaly","volume":"110","author":"Putrov","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1007\/JHEP11(2022)154","article-title":"Generalized symmetry breaking scales and weak gravity conjectures","volume":"11","author":"Cordova","year":"2022","journal-title":"J. High Energy Phys."},{"key":"ref_9","unstructured":"Cordova, C., Hong, S., and Koren, S. (2024). Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"161601","DOI":"10.1103\/PhysRevLett.133.161601","article-title":"Categorical Landau Paradigm for Gapped Phases","volume":"133","author":"Bhardwaj","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","unstructured":"Bhardwaj, L., Pajer, D., Schafer-Nameki, S., and Warman, A. (2024). Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries. arXiv."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"121601","DOI":"10.1103\/PhysRevLett.132.121601","article-title":"Quantization of Axion-Gauge Couplings and Noninvertible Higher Symmetries","volume":"132","author":"Choi","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1007\/JHEP12(2024)104","article-title":"The axion is going dark","volume":"12","author":"Dierigl","year":"2024","journal-title":"J. High Energy Phys."},{"key":"ref_14","unstructured":"Warman, A., Yang, F., Tiwari, A., Pichler, H., and Schafer-Nameki, S. (2024). Categorical Symmetries in Spin Models with Atom Arrays. arXiv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1016\/0003-4916(57)90049-0","article-title":"Classical physics as geometry: Gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space","volume":"2","author":"Misner","year":"1957","journal-title":"Ann. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"084019","DOI":"10.1103\/PhysRevD.83.084019","article-title":"Symmetries and Strings in Field Theory and Gravity","volume":"83","author":"Banks","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1007\/s00220-021-04040-y","article-title":"Symmetries in quantum field theory and quantum gravity","volume":"383","author":"Harlow","year":"2021","journal-title":"Commun. Math. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"191601","DOI":"10.1103\/PhysRevLett.122.191601","article-title":"Constraints on Symmetries from Holography","volume":"122","author":"Harlow","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","unstructured":"McNamara, J., and Vafa, C. (2019). Cobordism Classes and the Swampland. arXiv."},{"key":"ref_20","unstructured":"McNamara, J., and Vafa, C. (2020). Baby Universes, Holography, and the Swampland. arXiv."},{"key":"ref_21","unstructured":"McNamara, J. (2021). Gravitational Solitons and Completeness. arXiv."},{"key":"ref_22","unstructured":"McNamara, J. (2022). The Kinematics of Quantum Gravity. [Ph.D. Thesis, Harvard University]."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/JHEP09(2021)036","article-title":"Topological violation of global symmetries in quantum gravity","volume":"9","author":"Yonekura","year":"2021","journal-title":"J. High Energy Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/JHEP04(2023)061","article-title":"Estimating global charge violating amplitudes from wormholes","volume":"4","author":"Bah","year":"2023","journal-title":"J. High Energy Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"046007","DOI":"10.1103\/PhysRevD.110.046007","article-title":"On the holographic dual of a topological symmetry operator","volume":"110","author":"Heckman","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bah, I., Jefferson, P., Roumpedakis, K., and Waddleton, T. (2024). Symmetry Operators and Gravity. arXiv.","DOI":"10.1007\/JHEP01(2024)117"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/JHEP11(2021)053","article-title":"Chern-Weil global symmetries and how quantum gravity avoids them","volume":"11","author":"Heidenreich","year":"2021","journal-title":"J. High Energy Phys."},{"key":"ref_28","unstructured":"Vafa, C. (2005). The String landscape and the swampland. arXiv."},{"key":"ref_29","unstructured":"Brennan, T.D., Carta, F., and Vafa, C. (2017). The String Landscape, the Swampland, and the Missing Corner. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1900037","DOI":"10.1002\/prop.201900037","article-title":"The Swampland: Introduction and Review","volume":"67","author":"Palti","year":"2019","journal-title":"Fortsch. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2022.09.002","article-title":"Lectures on the Swampland Program in String Compactifications","volume":"989","author":"Mirfendereski","year":"2022","journal-title":"Phys. Rep."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Gra\u00f1a, M., and Herr\u00e1ez, A. (2021). The Swampland Conjectures: A Bridge from Quantum Gravity to Particle Physics. Universe, 7.","DOI":"10.3390\/universe7080273"},{"key":"ref_33","unstructured":"Agmon, N.B., Bedroya, A., Kang, M.J., and Vafa, C. (2022). Lectures on the string landscape and the Swampland. arXiv."},{"key":"ref_34","first-page":"60","article-title":"The String landscape, black holes and gravity as the weakest force","volume":"6","author":"Motl","year":"2007","journal-title":"J. High Energy Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"035003","DOI":"10.1103\/RevModPhys.95.035003","article-title":"Weak gravity conjecture","volume":"95","author":"Harlow","year":"2023","journal-title":"Rev. Mod. Phys."},{"key":"ref_36","unstructured":"Etheredge, M., Heidenreich, B., Pittman, N., Rauch, S., Reece, M., and Rudelius, T. (2025). Confined monopoles and failure of the Lattice Weak Gravity Conjecture. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"024031","DOI":"10.1103\/PhysRevD.65.024031","article-title":"Scales of gravity","volume":"65","author":"Dvali","year":"2002","journal-title":"Phys. Rev. D"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1088\/1126-6708\/2002\/06\/051","article-title":"Large N bounds on, and compositeness limit of, gauge and gravitational interactions","volume":"6","author":"Veneziano","year":"2002","journal-title":"J. High Energy Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1002\/prop.201000009","article-title":"Black Holes and Large N Species Solution to the Hierarchy Problem","volume":"58","author":"Dvali","year":"2010","journal-title":"Fortsch. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"045027","DOI":"10.1103\/PhysRevD.77.045027","article-title":"Black Hole Bound on the Number of Species and Quantum Gravity at LHC","volume":"77","author":"Dvali","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1002\/prop.201000008","article-title":"Evaporation of Microscopic Black Holes in String Theory and the Bound on Species","volume":"58","author":"Dvali","year":"2010","journal-title":"Fortsch. Phys."},{"key":"ref_42","unstructured":"Dvali, G., and Gomez, C. (2010). Species and Strings. arXiv."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1002\/prop.201300002","article-title":"Black Hole Quantum Mechanics in the Presence of Species","volume":"61","author":"Dvali","year":"2013","journal-title":"Fortsch. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4310\/BPAM.2024.v1.n1.a1","article-title":"Moduli-dependent species scale","volume":"1","author":"Vafa","year":"2024","journal-title":"Beijing J. Pure Appl. Math."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"138113","DOI":"10.1016\/j.physletb.2023.138113","article-title":"Black hole entropy and moduli-dependent species scale","volume":"844","author":"Cribiori","year":"2023","journal-title":"Phys. Lett. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/JHEP06(2023)047","article-title":"The emergence proposal in quantum gravity and the species scale","volume":"6","author":"Castellano","year":"2023","journal-title":"J. High Energy Phys."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/JHEP10(2023)145","article-title":"The emergence proposal and the emergent string","volume":"10","author":"Blumenhagen","year":"2023","journal-title":"J. High Energy Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2300150","DOI":"10.1002\/prop.202300150","article-title":"A Note on Modular Invariant Species Scale and Potentials","volume":"71","author":"Cribiori","year":"2023","journal-title":"Fortsch. Phys."},{"key":"ref_49","first-page":"112","article-title":"Species scale in diverse dimensions","volume":"5","author":"Vafa","year":"2024","journal-title":"J. High Energy Phys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2300143","DOI":"10.1002\/prop.202300143","article-title":"Bounds on Species Scale and the Distance Conjecture","volume":"71","author":"Vafa","year":"2023","journal-title":"Fortsch. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/JHEP12(2024)019","article-title":"On the species scale, modular invariance and the gravitational EFT expansion","volume":"12","author":"Castellano","year":"2024","journal-title":"J. High Energy Phys."},{"key":"ref_52","unstructured":"Castellano, A. (2024). The Quantum Gravity Scale and the Swampland. [Ph.D. Thesis, University Autonoma of Madrid]."},{"key":"ref_53","unstructured":"Valeixo Bento, B., and Melo, J.a. (2025). EFT & Species Scale: Friends or foes?. arXiv."},{"key":"ref_54","unstructured":"Calder\u00f3n-Infante, J., Castellano, A., and Herr\u00e1ez, A. (2025). The Double EFT Expansion in Quantum Gravity. arXiv."},{"key":"ref_55","unstructured":"Costa, D., C\u00f3rdova, C., Del Zotto, M., Freed, D., G\u00f6dicke, J., Hofer, A., Jordan, D., Morgante, D., Moscrop, R., and Ohmori, K. (2024). Simons Lectures on Categorical Symmetries. arXiv."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1088\/1126-6708\/2000\/08\/050","article-title":"Supergravity flows and D-brane stability","volume":"8","author":"Denef","year":"2000","journal-title":"J. High Energy Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1088\/1126-6708\/2002\/10\/023","article-title":"Quantum quivers and Hall\/hole halos","volume":"10","author":"Denef","year":"2002","journal-title":"J. High Energy Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/JHEP03(2024)061","article-title":"Gopakumar-Vafa invariants and the Emergent String Conjecture","volume":"3","author":"Rudelius","year":"2024","journal-title":"J. High Energy Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1007\/JHEP10(2018)164","article-title":"Tensionless Strings and the Weak Gravity Conjecture","volume":"10","author":"Lee","year":"2018","journal-title":"J. High Energy Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1007\/JHEP02(2022)190","article-title":"Emergent strings from infinite distance limits","volume":"2","author":"Lee","year":"2022","journal-title":"J. High Energy Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/JHEP02(2022)096","article-title":"Emergent strings, duality and weak coupling limits for two-form fields","volume":"2","author":"Lee","year":"2022","journal-title":"J. High Energy Phys."},{"key":"ref_62","unstructured":"Demirtas, M., Rios-Tascon, A., and McAllister, L. (2022). CYTools: A Software Package for Analyzing Calabi-Yau Manifolds. arXiv."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/JHEP03(2023)109","article-title":"The desert and the swampland","volume":"3","author":"Long","year":"2023","journal-title":"J. High Energy Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1140\/epjc\/s10052-018-5811-3","article-title":"The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff","volume":"78","author":"Heidenreich","year":"2018","journal-title":"Eur. Phys. J. C"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Dall\u2019Agata, G., and Zagermann, M. (2021). Supergravity: From First Principles to Modern Applications, Springer Nature. Lecture Notes in Physics.","DOI":"10.1007\/978-3-662-63980-1"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/0370-2693(95)00891-N","article-title":"Eleven-dimensional supergravity compactified on Calabi-Yau threefolds","volume":"357","author":"Cadavid","year":"1995","journal-title":"Phys. Lett. B"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0370-2693(96)00270-5","article-title":"M theory on a Calabi-Yau manifold","volume":"375","author":"Ferrara","year":"1996","journal-title":"Phys. Lett. B"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/JHEP04(2024)121","article-title":"On the string landscape without hypermultiplets","volume":"4","author":"Baykara","year":"2024","journal-title":"J. High Energy Phys."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"2100125","DOI":"10.1002\/prop.202100125","article-title":"The Weak Gravity Conjecture and BPS Particles","volume":"69","author":"Alim","year":"2021","journal-title":"Fortsch. Phys."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Kim, H.C., Vafa, C., and Xu, K. (2024). Finite Landscape of 6d N=(1,0) Supergravity. arXiv.","DOI":"10.1007\/JHEP10(2024)217"},{"key":"ref_71","unstructured":"Fernandez-Melgarejo, J.J., Giorgi, G., Marques, D., and Rosabal, J.A. (2024). On Non Invertible Symmetries in Type IIB Supergravity. arXiv."},{"key":"ref_72","first-page":"102","article-title":"Non-invertible symmetries in supergravity","volume":"4","year":"2023","journal-title":"J. High Energy Phys."},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Heckman, J.J., McNamara, J., Montero, M., Sharon, A., Vafa, C., and Valenzuela, I. (2024). On the Fate of Stringy Non-Invertible Symmetries. arXiv.","DOI":"10.1103\/PhysRevD.110.106001"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1007\/JHEP10(2023)154","article-title":"Global symmetry-breaking and generalized theta-terms in Type IIB EFTs","volume":"10","author":"Grimm","year":"2023","journal-title":"J. High Energy Phys."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/4\/490\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:59:45Z","timestamp":1760029185000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/4\/490"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,25]]},"references-count":74,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["sym17040490"],"URL":"https:\/\/doi.org\/10.3390\/sym17040490","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,3,25]]}}}