Consistency of Kaluza-Klein sphere reductions of symmetric potentials

In a recent paper, the complete (nonlinear) Kaluza-Klein Ansatz for the consistent embedding of certain scalar plus gravity subsectors of gauged maximal supergravity in D=4, 5, and 7 was presented in terms of sphere reductions from D=11 or type-IIB supergravity. The scalar fields included in the truncations were the diagonal fields in the SL(N,R)/SO(N) scalar submanifolds of the full scalar sectors of the corresponding maximal supergravities, with N=8, 6, and 5. The embeddings were used for obtaining an interpretation of extremal D=4, 5, or 7 AdS domain walls in terms of distributed M-branes or D-branes in the higher dimensions. Although strong supporting evidence for the correctness of the embedding Anstze was presented, a full proof of the consistency was not given. Here we complete the proof by showing explicitly that the full set of higher-dimensional equations of motion is satisfied if and only if the lower-dimensional fields satisfy the relevant scalar plus gravity equations. 2000 The American Physical Society.

Consistency of Kaluza-Klein sphere reductions of symmetric potentials Academic Article