Consistent truncation of Kaluza-Klein theories

We show that a Kaluza-Klein theory can be truncated to a four-dimensional theory with a finite number of gauge and matter fields. The truncation is consistent with respect to four-dimensional coordinate and gauge transformations. We give a truncation of eleven-dimensional supergravity compactified on the round seven-sphere that is consistent under the bosonic symmetries of the theory. (orig.)