AdS and dS Braneworld Kaluza - Klein Reduction

We obtain new results for consistent braneworld Kaluza-Klein reductions, showing how we can derive four-dimensional N = 2 gauged supergravity " localised on the AdS 4 brane " as an exact embedding in five-dimensional N = 4 gauged supergravity. Similarly, we obtain five-dimensional N = 2 gauged supergravity localised on an AdS 5 brane as a consistent Kaluza-Klein reduction from six-dimensional N = 4 gauged supergravity. These embed-dings can be lifted to type IIB and massive type IIA supergravity respectively. The new AdS braneworld Kaluza-Klein reductions are generalisations of earlier results on braneworld reductions to ungauged supergravities. The lower-dimensional cosmological constant in our AdS braneworld reductions is an adjustable parameter, and so it can be chosen to be small enough to be phenomenologically realistic, even if the higher-dimensional one is of Planck scale. We also discuss analytic continuations to give a de Sitter gauged supergravity in four dimensions as a braneworld Kaluza-Klein reduction. We find that there are two distinct routes that lead to the same four-dimensional theory. In one, we start from a five-dimensional de Sitter supergravity, which itself arises from a Kaluza-Klein reduction of type IIB * supergravity on the hyperbolic 5-sphere. In the other, we start from AdS gauged supergravity in five dimensions, with an analytic continuation of the two 2-form potentials, and embed the four-dimensional de Sitter supergravity in that. The five-dimensional theory itself comes from an O(4, 3)/O(3, 2) reduction of Hull's type IIB 7+3 supergravity in ten dimensions.