Background geometry of DLCQ M theory on a [formula presented]-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 (Formula presented)-torus (Formula presented) implies the holographic description of the microscopic theory. This argument lets us identify the background geometries of DLCQ M theory on a (Formula presented)-torus; for (Formula presented) 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 (Formula presented) 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 (Formula presented) theory on a spatial circle with the rescaled Planck length, giving an understanding of the validity of the AdS-CFT correspondence.