New compactifications in seven and eleven dimensional supergravity theories

It is found that the N=4 gauged supergravity in d=7 spontaneously compactifies on direct product of anti-deSitter space (AdS) with a 3-sphere (non-supersymmetric: N=0), or with 3-hyperboloid (N=2). Similarly the N=2 gauged supergravity in d=7 compactifies on AdSxH3(N=1). The possibility of σ-model induced compactification of ungauged d=7 N=2 supergravity coupled to one vector multiplet on (Minkowski)4 x Tear Drop x S1 is discussed. The case of d=11 supergravity is also studied, and two new compactifications are found: AdS x non-Einstein squashed S7(n=0) and AdS x non-Einstein SU(2) bundle over CP2(N=0). (author)