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

TL;DR

This paper explores the background geometries of DLCQ M theory on a p-torus and demonstrates their holographic duals, extending the AdS/CFT correspondence to various compactifications and providing insights into the microscopic theory.

Contribution

It identifies the background geometries of DLCQ M theory on a p-torus for p<5 and connects them with their holographic duals, clarifying the validity of AdS/CFT in this context.

Findings

For p=0, background is 11D Minkowski space.

For p=1, background is 10D Minkowski space.

For p=2,3,4, backgrounds are AdS space times spheres.

Abstract

Via supergravity, we argue that the infinite Lorentz boost along the M theory circle a la 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 $\tilde{M}$ theory on a spatial circle with the rescaled Planck length, giving an understanding of the validity of the AdS/CFT correspondence.