Consistent SO(6) Reduction Of Type IIB Supergravity on S^5

TL;DR

The paper constructively derives a complete non-linear Kaluza-Klein reduction of Type IIB supergravity on S^5 that preserves gravity, all 15 SO(6) gauge fields, and the 20 scalars in SL(6,R)/SO(6), yielding a consistent embedding into D=10 and clarifying the role of the self-dual 5-form. It also establishes general constraints on when gravity plus an antisymmetric tensor can admit consistent sphere reductions, showing that only D=11 with a 4-form and D=10 with a self-dual 5-form are viable, with D=11 providing the full bosonic structure and D=10 singled out for retaining only gravity plus the 5-form and gauge fields. Through truncations to known sectors, the authors connect their Ansatz to existing D=5 gauged supergravity embeddings and verify consistency with prior results. The work highlights the necessity of including gauge fields when the scalars are nonzero and underscores self-duality as a structural requirement for sphere reductions. These results have implications for AdS/CFT embeddings and the landscape of consistent Kaluza-Klein reductions in string/M‑theory.

Abstract

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.