Freund-Rubin compactification
Encyclopedia
11D supergravity
contains a 3-form field C. It also contains an electric 2-brane (M2) and a magnetic 5-brane (M5) under C. These branes are BPS
states and they are also black brane
s. Their near horizon metrics are given by AdS4×S7 and AdS7× S4 respectively. These geometries contain a nonzero four-flux which gives rise to a nonzero Ricci curvature
. They are called Freund–Rubin compactifications.
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...
contains a 3-form field C. It also contains an electric 2-brane (M2) and a magnetic 5-brane (M5) under C. These branes are BPS
BPS
BPS can stand for:In science, mathematics and technology*Base pairs, a measure of length of DNA using the number of nucleotide pairs*Basis points, equal to one one-hundredth of a percentage point...
states and they are also black brane
Black brane
In general relativity, a black brane is a solution of the equations that generalizes a black hole solution but it is also extended —and translationally symmetric— in p additional spatial dimensions...
s. Their near horizon metrics are given by AdS4×S7 and AdS7× S4 respectively. These geometries contain a nonzero four-flux which gives rise to a nonzero Ricci curvature
Ricci curvature
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume element of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space...
. They are called Freund–Rubin compactifications.