2002/08/31 by Changhyun Ahn, Taichi Itoh · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #hep-th
paper · pdf · doi:10.1016/s0550-3213(02)00871-4
published as Nucl.Phys. B646 (2002) 257-280 · 26 pp, the second and fourth paragraphs of the introduction improved and to appear in NPB
arxiv created 2002/09/25 · openalex publication_date 2002/11/12 · arxiv updated 2010/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)xU(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.