Time-Dependent Supersymmetric Solutions in M-Theory and the Compactification-Decompactification Transition

TL;DR

This paper generalizes supersymmetric light-like solutions in M-theory to include non-diagonal cases, enabling the construction of smooth transitions between compactified and decompactified regions in spacetime.

Contribution

It introduces a broader class of supersymmetric solutions in eleven-dimensional supergravity, facilitating models of dynamic compactification and decompactification.

Findings

Constructed non-diagonal supersymmetric solutions

Demonstrated smooth transition between compactified and decompactified regions

Extended previous solutions to include spatial-coordinate dependence

Abstract

We show that the diagonal light-like solution with 16 supersymmetries in eleven-dimensional supergravity derived in our previous paper (hep-th/0509173) can be generalised to non-diagonal solutions preserving the same number of supersymmetries. This class of solutions contains a subclass equivalent to the class of solutions found by Bin Chen that are dependent on the spatial-coordinates. Utilising these solutions, we construct toroidally compactified solutions that smoothly connect a static compactified region with a dynamically decompactifying region along a null hypersurface.