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Register a new user11D Supergravity on $AdS_4 times S^7$ versus $AdS_7 times S^4$
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Authors
Ergin Sezgin
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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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We present a constructive derivation of all four-point tree-level holographic correlators for eleven dimensional supergravity on $AdS_7 times S^4$. These correlators correspond to four-point functions of arbitrary one-half BPS operators in the six-dimensional $(2,0)$ theory at large central charge. The crucial observation is that the polar part of the correlators in Mellin space is fully captured by a drastically simpler Maximally R-symmetry Violating (MRV) amplitude, while the contact part is fully fixed by superconformal Ward identities and the flat space limit.
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