S-3 and S-4 reductions of type IIA supergravity

We construct a consistent reduction of type IIA supergravity on S-3, leadin g to a maximal gauged supergravity in seven dimensions with the full set of massless SO(4) Yang-Mills fields. We do this by starting with the known S- 4 reduction of eleven-dimensional supergravity, and showing that it is poss ible to take a singular limit of the resulting standard SO(5)-gauged maxima l supergravity in seven dimensions, whose eleven-dimensional interpretation involves taking a limit where the internal 4-sphere degenerates to R x S-3 . This allows us to reinterpret the limiting SO(4)-gauged theory in seven d imensions as the S-3 reduction of type IIA supergravity. We also obtain the consistent S-4 reduction of type IIA supergravity, which gives an SO(S)-ga uged maximal supergravity in D = 6. (C) 2000 Elsevier Science B.V. All righ ts reserved.