Four-dimensional Einstein Yang–Mills de Sitter gravity from eleven dimensions

AbstractWe obtain D=4 de Sitter gravity coupled to SU(2) Yang–Mills gauge fields from an explicit and consistent truncation of D=11 supergravity via Kaluza–Klein dimensional reduction on a non-compact space. The “internal” space is a smooth hyperbolic 7-space (H7) written as a foliation of two 3-spheres, on which the SU(2) Yang–Mills fields reside. The positive cosmological constant is completely fixed by the SU(2) gauge coupling constant. The explicit reduction ansatz enables us to lift any of the D=4 solutions to D=11. In particular, we obtain dS2 in M-theory, where the nine-dimensional transverse space is an H7 bundle over S2. We also obtain a new smooth embedding of dS3 in D=6 supergravity