The Background Geometry of DLCQ Supergravity

TL;DR

This paper describes the background geometries of DLCQ supergravity related to M-theory compactified on tori, highlighting their symmetry properties and supersymmetry, and suggesting a connection to M/string theory on these backgrounds.

Contribution

It provides explicit background geometries for DLCQ supergravity of M-theory on tori, showing their symmetry and supersymmetry properties, and linking them to M/string theory.

Findings

Geometries are products of anti-de Sitter spaces and spheres.

These geometries preserve all 32 supersymmetries.

They correspond to known supergravity compactifications and near horizon limits.

Abstract

By following Seiberg's prescriptions on DLCQ of $M$ theory, we give the background geometries of DLCQ supergravity associated with $N$ sector of DLCQ of $M$ theory on $T^p$ with vanishingly small radii. Most of these are the product of anti-de Sitter spacetimes and spheres, which have been found as the spontaneous compactifications of eleven dimensional supergravity long time ago and also are revisited recently by Maldacena by considering the near horizon geometry of various D-branes in appropriate limit. Those geometries are maximally symmetric and have full 32 supersymmetries of eleven dimensional supergravity, which agrees with the number of supersymmetries of DLCQ of $M$ theory. This suggests that DLCQ of $M$ theory is the $M$/string theory on these nontrivial background.