Five-dimensional N=4, SU(2) X U(1) Gauged Supergravity from Type IIB

TL;DR

This work delivers a complete, explicit all-orders non-linear Kaluza-Klein reduction of type IIB supergravity on $S^5$ that reproduces the bosonic sector of $D=5$, $\mathcal{N}=4$ $SU(2)\times U(1)$ gauged supergravity (Romans theory), including non-abelian gauge fields and a charged doublet of 2-forms. By leveraging a non-abelian extension of the $S^5$ metric using left-invariant $SU(2)$ forms and a complex 2-form $\hat{A}_{(2)}$, the authors derive a consistent reduction where the ten-dimensional equations of motion precisely yield the $D=5$ Romans equations, with a first-order equation for $A_{(2)}$ and a covariant equation $D(X^{2}\,{*F_{(3)}})=g^{2}\, X^{-2}\,{*A_{(2)}}$. The construction, including fixed dilaton/axion moduli, enables uplifting any bosonic solution of the $D=5$ theory to a $D=10$ solution and constitutes the first fully consistent $S^5$ reduction that includes non-abelian gauge fields, reinforcing the AdS/CFT framework and suggesting avenues toward a full $SO(6)$ gauged $N=8$ reduction. Overall, the paper provides a powerful tool for embedding five-dimensional solutions in type IIB and for clarifying the role of truncations in holographic computations.

Abstract

We construct the complete and explicit non-linear Kaluza-Klein ansatz for deriving the bosonic sector of N=4 SU(2)\times U(1) gauged five-dimensional supergravity from the reduction of type IIB supergravity on S^5. This provides the first complete example of such an S^5 reduction that includes non-abelian gauge fields, and it allows any bosonic solution of the five-dimensional N=4 gauged theory to be embedded in D=10.