TY - JOUR
T1 - A classification of compactifying solutions for d =11 supergravity
AU - Castellani, L.
AU - Romans, L. J.
AU - Warner, N. P.
N1 - Funding Information:
* Work supported in part by the US Department of Energy under contract no DEAC-03-81-ER40050 1 On leave from the Inst~tuto Nazlonale di Flsica Nucleare Tormo Umverslty Work supported in part by the Flelschmann Foundation 2 Wemgart Foundation Fellow ** A mamfold is defined to be Einstein if its Rlccl tensor is proportional to its metric tensor
PY - 1984/7/23
Y1 - 1984/7/23
N2 - Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail. The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry. The existence of a spin structure on homogeneous manifolds G H is discussed and related to topological properties of G H. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.
AB - Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail. The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry. The existence of a spin structure on homogeneous manifolds G H is discussed and related to topological properties of G H. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.
UR - http://www.scopus.com/inward/record.url?scp=0001010461&partnerID=8YFLogxK
U2 - 10.1016/0550-3213(84)90055-5
DO - 10.1016/0550-3213(84)90055-5
M3 - Article
SN - 0550-3213
VL - 241
SP - 429
EP - 462
JO - Nuclear Physics B
JF - Nuclear Physics B
IS - 2
ER -