We define the notion of Y-algebroids, generalising the Lie, Courant, and exceptional algebroids that have been used to capture the local symmetry structure of type II string theory and M-theory compactifications to D ≥ 5 dimensions. Instead of an invariant inner product, or its generalisation arising in exceptional algebroids, Y-algebroids are built around a specific type of tensor, denoted Y , that provides exactly the necessary properties to also describe compactifications to D = 4 dimensions. We classify “M-exact” E 7-algebroids and show that this precisely matches the form of the generalised tangent space of E 7(7) × ℝ+-generalised geometry, with possible twists due to 1-, 4- and 7-form fluxes, corresponding physically to the derivative of the warp factor and the M-theory fluxes. We translate the notion of generalised Leibniz parallelisable spaces, relevant to consistent truncations, into this language, where they are mapped to so-called exceptional Manin pairs. We also show how to understand Poisson-Lie U-duality and exceptional complex structures using Y-algebroids.
{ "_oai": { "updated": "2024-06-24T00:33:07Z", "id": "oai:repo.scoap3.org:83880", "sets": [ "JHEP" ] }, "authors": [ { "affiliations": [ { "country": "Belgium", "value": "Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, B-1050, Belgium", "organization": "Vrije Universiteit Brussel" } ], "surname": "Hul\u00edk", "email": "ondra.hulik@gmail.com", "full_name": "Hul\u00edk, Ond\u0159ej", "given_names": "Ond\u0159ej" }, { "affiliations": [ { "country": "Germany", "value": "Institut f\u00fcr Physik, Humboldt-Universit\u00e4t zu Berlin, IRIS Geb\u00e4ude, Zum Gro\u00dfen Windkanal 2, Berlin, 12489, Germany", "organization": "Institut f\u00fcr Physik, Humboldt-Universit\u00e4t zu Berlin, IRIS Geb\u00e4ude" } ], "surname": "Malek", "email": "emanuel.malek@physik.hu-berlin.de", "full_name": "Malek, Emanuel", "given_names": "Emanuel" }, { "affiliations": [ { "country": "UK", "value": "Department of Physics, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK", "organization": "Imperial College London" } ], "surname": "Valach", "email": "fridrich.valach@gmail.com", "full_name": "Valach, Fridrich", "given_names": "Fridrich" }, { "affiliations": [ { "country": "UK", "value": "Department of Physics, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK", "organization": "Imperial College London" } ], "surname": "Waldram", "email": "d.waldram@imperial.ac.uk", "full_name": "Waldram, Daniel", "given_names": "Daniel" } ], "titles": [ { "source": "Springer", "title": "Y-algebroids and E 7(7) \u00d7 \u211d+-generalised geometry" } ], "dois": [ { "value": "10.1007/JHEP03(2024)034" } ], "publication_info": [ { "page_end": "23", "journal_title": "Journal of High Energy Physics", "material": "article", "journal_volume": "2024", "artid": "JHEP03(2024)034", "year": 2024, "page_start": "1", "journal_issue": "3" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2024-06-24T00:31:29.917619", "source": "Springer", "method": "Springer", "submission_number": "e40b131a31c011ef9fecbe60ec5a7b90" }, "page_nr": [ 23 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2024" } ], "control_number": "83880", "record_creation_date": "2024-03-07T03:30:07.162902", "_files": [ { "checksum": "md5:da26dc91aa168cae10630555e4be79a2", "filetype": "xml", "bucket": "10f5f146-6cc0-4969-83d9-4d861333eb9e", "version_id": "83671799-a548-4352-843c-4929a3d6cd3a", "key": "10.1007/JHEP03(2024)034.xml", "size": 14167 }, { "checksum": "md5:f5be8f9dffd8955732e179016ff5f283", "filetype": "pdf/a", "bucket": "10f5f146-6cc0-4969-83d9-4d861333eb9e", "version_id": "b05193a0-d342-45c5-a5a8-3f259ac4bf3b", "key": "10.1007/JHEP03(2024)034_a.pdf", "size": 414170 } ], "collections": [ { "primary": "Journal of High Energy Physics" } ], "arxiv_eprints": [ { "categories": [ "hep-th", "math-ph", "math.DG", "math.MP" ], "value": "2308.01130" } ], "abstracts": [ { "source": "Springer", "value": "We define the notion of Y-algebroids, generalising the Lie, Courant, and exceptional algebroids that have been used to capture the local symmetry structure of type II string theory and M-theory compactifications to D \u2265 5 dimensions. Instead of an invariant inner product, or its generalisation arising in exceptional algebroids, Y-algebroids are built around a specific type of tensor, denoted Y , that provides exactly the necessary properties to also describe compactifications to D = 4 dimensions. We classify \u201cM-exact\u201d E 7-algebroids and show that this precisely matches the form of the generalised tangent space of E 7(7) \u00d7 \u211d+-generalised geometry, with possible twists due to 1-, 4- and 7-form fluxes, corresponding physically to the derivative of the warp factor and the M-theory fluxes. We translate the notion of generalised Leibniz parallelisable spaces, relevant to consistent truncations, into this language, where they are mapped to so-called exceptional Manin pairs. We also show how to understand Poisson-Lie U-duality and exceptional complex structures using Y-algebroids." } ], "imprints": [ { "date": "2024-03-06", "publisher": "Springer" } ] }