Abstract
In this paper, we present a unified perspective on sphere consistent truncations based on the classical geometric properties of sphere bundles. The backbone of our approach is the global angular form for the sphere. A universal formula for the Kaluza-Klein ansatz of the flux threading the n-sphere captures the full nonabelian isometry group SO(n + 1) and scalar deformations associated to the coset SL(n + 1, ℝ)/SO(n + 1). In all cases, the scalars enter the ansatz in a shift by an exact form. We find that the latter can be completely fixed by imposing mild conditions, motivated by supersymmetry, on the scalar potential arising from dimensional reduction of the higher dimensional theory. We comment on the role of the global angular form in the derivation of the topological couplings of the lower-dimensional theory, and on how this perspective could provide inroads into the study of consistent truncations with less supersymmetry.
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Acknowledgments
We thank M. Duff, C. Hull, and D. Waldram for useful discussions and correspondence. RM is supported in part by ERC Grant 787320-QBH Structure and by ERC Grant 772408-Stringlandscape. The work of VVC was supported by the Alexander von Humboldt Foundation via a Feodor Lynen fellowship. The work of FB is supported by the Simons Collaboration Grant on Categorical Symmetries. PW is supported in part by NSF grant PHY-2112699.
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Bonetti, F., Minasian, R., Camell, V.V. et al. Consistent truncations from the geometry of sphere bundles. J. High Energ. Phys. 2023, 156 (2023). https://doi.org/10.1007/JHEP05(2023)156
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DOI: https://doi.org/10.1007/JHEP05(2023)156