Consistent SO(6) reduction of type IIB supergravity on S5

Type IIB supergravity can be consistently truncated to the metric and the self-dual. 5-form. We obtain the complete non-linear Kaluza-Klein S-5 reduction ansatz for this theory, giving rise to gravity coupled to the fifteen Yang-Mills gauge fields of SO(6) and the twenty scalars of the coset SL(6, R)/SO(6). This provides a consistent embedding of this subsector of N = 8, D = 5 gauged supergravity in type IIB in D = 10. We demonstrate that the self-duality of the 5-form plays a crucial role in the consistency of the reduction. We also discuss certain necessary conditions for a theory of gravity and an antisymmetric tensor in an arbitrary dimension D to admit a consistent sphere reduction, keeping all the massless fields. We find that it is only possible for D = 11, with a 4-form field, and D = 10, with a 5-form. Furthermore, in D = 11 the full bosonic structure of eleven-dimensional supergravity is required, while in D = 10 the 5-form must be self-dual. It is remarkable that just from the consistency requirement alone one would discover D = 11 and type IIB supergravities, and that D = 11 is an upper bound on the dimension. (C) 2000 Elsevier Science B.V. All rights reserved.