TY - JOUR
T1 - Einstein metrics on homogeneous spaces, and d = 11 supergravity
AU - Castellani, Leonardo
N1 - Funding Information:
all other components vanishing \[2\]F. uvaa is the curl of the three-index antisymmetric tensor of eleven-di. mensional supergravity. Eqs. (1) describe a four-dimensional spacetime M 4 with negative cosmological con. stant (for example anti-De Sitter spacetime), and a seven-dimensional Einstein space M 7 with positive curvature. The compactification on M 4 X M 7 is triggered by the nonzero value of F~vaa: the fourth-rank "photon" curl of d = 11 supergravity forces spacetime to have four dimensions \[2\]. Spaces with the Ricci tensor proportional to the metric are called Einstein spaces * 1. To every seven-dimensional Einstein space M 7 corresponds a solution M 4 X M 7 of the field equations ofd = 11 supergravity. Reducing the theory to four dimensions through the 1 On leave from the Istituto Nazionale di Fisica Nucleate, Torino University, Turin, Italy. Work supported in part by the US Department of Energy under contract DEAC 03-81-ER40050 and the Fleisehmann Foundation. ,1 A recent discussion on Einstein metrics can be found in ref. \[31.
PY - 1984/12/13
Y1 - 1984/12/13
N2 - We prove that every compact homogeneous space G/H, with maximal H and inequivalent isotropy representations, admits at least one Einstein metric. This has an interesting implication for d = 11 supergravity, as every compact seven-dimensional Einstein space provides a Freund-Rubin solution of the type (anti-De Sitter spacetime) × G/H.
AB - We prove that every compact homogeneous space G/H, with maximal H and inequivalent isotropy representations, admits at least one Einstein metric. This has an interesting implication for d = 11 supergravity, as every compact seven-dimensional Einstein space provides a Freund-Rubin solution of the type (anti-De Sitter spacetime) × G/H.
UR - https://www.scopus.com/pages/publications/48549112987
U2 - 10.1016/0370-2693(84)91562-4
DO - 10.1016/0370-2693(84)91562-4
M3 - Article
SN - 0370-2693
VL - 149
SP - 103
EP - 106
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
IS - 1-3
ER -