Y-algebroids and E 7(7) × ℝ+-generalised geometry

Ondřej Hulík (Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, Brussels, B-1050, Belgium) ; Emanuel Malek (Institut für Physik, Humboldt-Universität zu Berlin, IRIS Gebäude, Zum Großen Windkanal 2, Berlin, 12489, Germany) ; Fridrich Valach (Department of Physics, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK) ; Daniel Waldram (Department of Physics, Imperial College London, Prince Consort Road, London, SW7 2AZ, UK)

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.

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      "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."
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Published on:
06 March 2024
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2024 (2024)
Issue 3
Pages 1-23
DOI:
https://doi.org/10.1007/JHEP03(2024)034
arXiv:
2308.01130
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: