Abstract
The connection between two recent descriptions of tensor hierarchies — namely, infinity-enhanced Leibniz algebroids, given by Bonezzi & Hohm and Lavau & Palmkvist, and the p-brane QP-manifolds constructed by Arvanitakis — is made precise. This is done by presenting a duality-covariant version of latter.
The construction is based on the QP-manifold T⋆[n]T[1]M × ℋ[n], where M corresponds to the internal manifold of a supergravity compactification and ℋ[n] to a degree-shifted version of the infinity-enhanced Leibniz algebroid. Imposing that the canonical Q-structure on T⋆[n]T[1]M is the derivative operator on ℋ leads to a set of constraints. Solutions to these constraints correspond to \( \frac{1}{2} \)-BPS p-branes, suggesting that this is a new incarnation of a brane scan. Reduction w.r.t. to these constraints reproduces the known p-brane QP-manifolds. This is shown explicitly for the SL(3)×SL(2)- and SL(5)-theories.
Furthermore, this setting is used to speculate about exceptional ‘extended spaces’ and QP-manifolds associated to Leibniz algebras. A proposal is made to realise differential graded manifolds associated to Leibniz algebras as non-Poisson subspaces (i.e. not Poisson reductions) of QP-manifolds similar to the above. Two examples for this proposal are discussed: generalised fluxes (including the dilaton flux) of O(d, d) and the 3-bracket flux for the SL(5)-theory.
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Acknowledgments
The author thanks Athanasios Chatzistavrakidis and Saskia Demulder for discussions initiating this project, Chris Blair and Sylvain Lavau for comments on the first version and acknowledges Dieter Lust and the Faculty of Physics of Ludwig Maximilian University Munich for their extraordinary support in the year 2022.
This research is part of the project No. 2022/45/P/ST2/03995 co-funded by the National Science Centre and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 945339.
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Osten, D. On exceptional QP-manifolds. J. High Energ. Phys. 2024, 28 (2024). https://doi.org/10.1007/JHEP01(2024)028
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DOI: https://doi.org/10.1007/JHEP01(2024)028