The 11-dimensional metric for AdS/CFT RG flows with common SU(3) invariance Original Research Article

The compact 7-manifold arising in the compactification of 11-dimensional supergravity is described by the metric encoded in the vacuum expectation values (vevs) in d=4, N=8 gauged supergravity. Especially, the space of SU(3)-singlet vevs contains various critical points and RG flows (domain walls) developing along AdS4 radial coordinate. Based on the nonlinear metric ansatz of de Wit–Nicolai–Warner, we show the geometric construction of the compact 7-manifold metric and find the local frames (siebenbeins) by decoding the SU(3)-singlet vevs into squashing and stretching parameters of the 7-manifold. Then the 11-dimensional metric for the whole SU(3)-invariant sector is obtained as a warped product of an asymptotically AdS4 space with a squashed and stretched 7-sphere. We also discuss the difference in the 7-manifold between two sectors, namely (SU(3)×U(1))-invariant sector and G2-invariant sector. In spite of the difference in base 6-sphere, both sectors share the 4-sphere of CP2 associated with the common SU(3)-invariance of various 7-manifolds.