D=5 SU(2)xU(1) Gauged Supergravity from D=11 Supergravity

TL;DR

The paper tackles the problem of obtaining a consistent KK reduction from $D=11$ supergravity on the general $AdS_5\\times_w{\\cal N}_6$ backgrounds (dual to $N=2$ SCFTs in $d=4$) to Romans' $D=5$ $SU(2)\\times U(1)$ gauged supergravity by constructing a full non-linear bosonic KK ansatz. This ansatz, valid for any ${\\cal N}_6$ in the Lin-Lunin-Maldacena class, enables uplifting of any $D=5$ solution to an $D=11$ solution and is anchored by an explicit ${\\cal N}_6$ corresponding to M5-branes wrapping holomorphic curves in a Calabi-Yau two-fold. The authors illustrate the construction by uplifting several explicit $D=5$ solutions (Nieder-Oz, Maldacena-Núñez, Klemm-Sabra, and magnetovac configurations) to $D=11$, obtaining new wrapped-brane geometries and clarifying their holographic interpretations as RG flows between AdS spacetimes and lower-dimensional CFTs. These results provide substantial evidence for a broad class of consistent KK truncations and lay groundwork for extending the framework to fermions and to type IIB analogues, strengthening the link between higher- and lower-dimensional supergravity descriptions of wrapped-brane SCFTs.

Abstract

We consider the most general class of supersymmetric solutions of D=11 supergravity consisting of a warped product of AdS_5 with a six-dimensional internal manifold N_6, which are dual to N=2 super conformal field theories in d=4. For any such N_6 we construct the full non-linear Kaluza-Klein ansatz for the reduction of D=11 supergravity on N_6 down to D=5 SU(2)xU(1) gauged supergravity, at the level of the bosonic fields. This allows one to uplift any solution of the D=5 supergravity to obtain a solution of D=11 supergravity for any given N_6. Using an explicit N_6, corresponding to M5-branes wrapping holomorphic curves in a Calabi-Yau two-fold, we uplift some solutions and comment upon their interpretation.