Background geometry of DLCQ M theory on a p-torus and holography

Via supergravity, we argue that the infinite Lorentz boost along the M theory circle in the manner of Seiberg toward the DLCQ M theory compactified on a p-torus (p<5) implies the holographic description of the microscopic theory. This argument lets us identify the background geometries of DLCQ M theory on a p-torus; for p=0 (p=1), the background geometry turns out to be eleven-dimensional (ten-dimensional) flat Minkowski space-time, respectively. Holography for these cases results from the localization of the light-cone momentum. For p=2,3,4, the background geometries are the tensor products of an anti-de Sitter space and a sphere, which, according to the AdS-CFT correspondence, have the holographic conformal field theory description. These holographic descriptions are compatible to the microscopic theory of Seiberg based on M theory on a spatial circle with the rescaled Planck length, giving an understanding of the validity of the AdS-CFT correspondence.