On supersymmetric AdS6 solutions in 10 and 11 dimensions

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We prove a non-existence theorem for smooth, supersymmetric, warped AdS6 solutions with connected, compact without boundary internal space in D=11 and (massive) IIA supergravities.

• In IIB supergravity we show that if such AdS6 solutions exist, then the NSNS and RR 3-form fluxes must be linearly independent and certain spinor bi-linears must be appropriately restricted.
• Moreover we demonstrate that the internal space admits an so(3) action which leaves all the fields invariant and for smooth solutions the principal orbits must have co-dimension two.
• We also describe the topology and geometry of internal spaces that admit such a so(3) action and show that there are no solutions for which the internal space has topology F * S^2, where F is an oriented surface.