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11D Supergravity on $AdS_4 \times S^7$ versus $AdS_7 \times S^4$

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arxiv 2003.01135 v1 pith:ELCRVQZL submitted 2020-03-02 hep-th

Ergin Sezgin This is my paper · ORCID
classification hep-th
keywords timescontinuationkaluza-kleinsupergravityvacuaadmitanalyticanalytical
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abstract

The maximally supersymmetric Freund-Rubin vacua for eleven dimensional supergravity, namely $AdS_4 \times S^7$ and $AdS_7 \times S^4$, admit an analytic continuation to $S^4 \times S^7$. From the full harmonic expansions on $S^4 \times S^7$, it is shown that by analytical continuation to either $AdS_4$, or to $AdS_7$, the detailed structure of the Kaluza-Klein spectrum can be obtained for both vacua in a unified manner. The results are shown to be related by a simple rule which interchanges the spacetime and internal space representations. We also obtain the linearized field equations for the singletons and doubletons but they can be gauged away by fixing certain Stuckelberg shift symmetries inherited from the Kaluza-Klein reduction.

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Cited by 4 Pith papers

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  3. Squashed 7-spheres, octonions and the swampland

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    The complete Kaluza-Klein operator spectrum on the squashed S7 in eleven-dimensional supergravity is reviewed, with emphasis on 2-form modes, singletons, and a speculative singleton Higgsing effect relevant to the AdS...

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    This invited review recounts the S7 compactifications of eleven-dimensional supergravity and summarises recent spectral results, including a speculative singleton Higgs mechanism.

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