Abstract
The squashed seven-sphere operator spectrum is completed by deriving the spectrum of the spin-3/2 operator. The implications of the results for the AdS4 \( \mathcal{N} \) = 1 supermultiplets obtained from compactification of eleven-dimensional supergravity are analysed. The weak G2 holonomy plays an important role when solving the eigenvalue equations on the squashed sphere. Here, a novel and more universal algebraic approach to the whole eigenvalue problem on coset manifolds is provided. Having obtained full control of all the operator spectra, we can finally determine the irreps D(E0, s) for all supermultiplets in the left-squashed vacuum. This includes an analysis of possible boundary conditions. By performing an orientation flip on the seven-sphere, we also obtain the full spectrum for the non-supersymmetric right-squashed compactification which is of interest in the swampland context and in particular for the AdS swampland conjecture. Here, a number of boundary condition ambiguities arise making the analysis of dual marginal operators somewhat involved. This work is a direct continuation of [1] and [2].
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Acknowledgments
J.K. thanks Junho Hong, Emanuel Malek, Henning Samtleben, Thomas Van Riet and, in particular, Nikolay Bobev for useful comments and discussions. The second author, B.E.W.N., is grateful to Mike Duff and Chris Pope for many discussions and collaboration at an early stage of this work. We are also grateful to Igor Klebanov and the referee for discussions and comments on parts of the manuscript. J.K. is supported by the Research Foundation - Flanders (FWO) doctoral fellowship 1171823N and, in part, by the FWO research grants G092617N and G0H9318N. B.E.W.N. is partly supported by the Wilhelm and Martina Lundgren Foundation.
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Karlsson, J., Nilsson, B.E.W. The complete Kaluza-Klein spectra of \( \mathcal{N} \) = 1 and \( \mathcal{N} \) = 0 M-theory on AdS4 × (squashed S7). J. High Energ. Phys. 2024, 144 (2024). https://doi.org/10.1007/JHEP02(2024)144
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DOI: https://doi.org/10.1007/JHEP02(2024)144