Compactifications of \(d=11\) supergravity on Kähler manifolds (Q1116481)

We consider compactifications of eleven-dimensional supergravity to five and three space-time dimensions, on interval spaces \(K_ 6\) and \(K_ 2\times K_ 6\), where \(K_ n\) denotes an n-dimensional Kähler manifold. The compactifications to five dimensions yield no surviving space-time supersymmetries. However, we find compactifications to three dimensions on \(S^ 2\times K_ 6\) and \(T^ 2\times K_ 6\) where \(K_ 6\) is Ricci-flat and Kähler (a Calabi-Yau space) with \(N=4\) supersymmetry. We also discuss the massless spectrum.