Universal Kaluza-Klein reductions of type IIB to N=4 supergravity in five dimensions

TL;DR

This work constructs explicit universal Kaluza-Klein reductions of type IIB supergravity on $HK_4\times S^1$ and on $SE_5$, producing $D=5$ theories with $N=4$ supersymmetry. The $HK_4\times S^1$ reduction yields $D=5$ $N=4$ ungauged supergravity coupled to two vector multiplets, while the $SE_5$ reduction yields a $D=5$ $N=4$ gauged supergravity (two vector multiplets) that includes the breathing mode; the gauging is $H_3\times U(1)\subset SO(5,2)$ and the non-closure of the $SE_5$ structure drives it. Both reductions admit supersymmetric $AdS_5$ vacua uplifting to $AdS_5\times SE_5$ (with spontaneous breaking $N=4\to N=2$) and a Romans-type non-supersymmetric AdS$_5$ vacuum. The authors further show how various consistent truncations reproduce known five-dimensional theories (e.g., Maldacena 2008, Gubser 2009qm) and discuss potential generalizations to other geometries and higher-dimensional reductions, highlighting the utility of these universal sectors for holographic applications.

Abstract

We construct explicit consistent Kaluza-Klein reductions of type IIB supergravity on HK_4 x S^1, where HK_4 is an arbitrary four-dimensional hyper-Kaehler manifold, and on SE5, an arbitrary five-dimensional Sasaki-Einstein manifold. In the former case we obtain the bosonic action of D=5 N=4 (ungauged) supergravity coupled to two vector multiplets. For the SE_5 case we extend a known reduction, which leads to minimal D=5 N=2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the SE_5. We show that the resulting D=5 action is also consistent with N=4 gauged supergravity coupled to two vector multiplets. This theory has a supersymmetric AdS_5 vacuum, which uplifts to the class of supersymmetric AdS_5 x SE_5 solutions, that spontaneously breaks N=4 to N=2, and also a non-supersymmetric AdS_5 vacuum which uplifts to a class of solutions first found by Romans.