Hopf fibration of eleven-dimensional supergravity

Abstract

The authors show that all known solutions of the N=2 non-chiral d=10 supergravity theory can, by a simple procedure, be obtained from the known Freund-Rubin type solutions of D=11 supergravity. This is a consequence of the fact that each solution of the d=10 theory depends crucially on the presence of a topologically non-trivial U(1) field strength Fmn. The mass spectrum of a particular d=10 solution is obtained by truncating the spectrum of the corresponding d=11 solution to the subset of fields neutral under the non-trivial U(1) symmetry. They investigate the compactification on CP3, and show that this yields a theory with N=6 or N=0 supersymmetry according to the orientation, and they relate this to the S7 compactification of d=11 supergravity. Starting from the squashed S7 in d=11 they derive a new solution of the d=10 theory, namely (AdS)4 times CP3 with a squashed non-Einstein metric. The supersymmetry is either N=1 or N=0 depending on the orientation. They conjecture that none of the supergravity theories in 4<d<10 dimensions obtained from d=11 by dimensional reduction admit non-trivial compactifications to four dimensions.