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

TL;DR

This paper derives a complete non-linear Kaluza-Klein reduction ansatz for type IIB supergravity on S^5, embedding a subsector of five-dimensional gauged supergravity into ten dimensions, emphasizing the role of self-duality in the reduction's consistency.

Contribution

It provides the first explicit non-linear reduction ansatz for type IIB supergravity on S^5, including all relevant fields and the crucial self-duality condition, establishing conditions for consistent sphere reductions.

Findings

Complete non-linear S^5 reduction ansatz derived

Self-duality of the 5-form is essential for consistency

Only D=11 and D=10 allow consistent sphere reductions

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.