# M-theory from the Superpoint

## TL;DR

This paper demonstrates that super-Minkowski spacetimes, fundamental to string and M-theory, can be systematically derived as maximal invariant central extensions starting from the superpoint, revealing their deep algebraic structure.

## Contribution

It provides a systematic method to derive super-Minkowski spacetimes from the superpoint via maximal invariant central extensions, connecting algebraic structures to string/M-theory.

## Key findings

- Super-Minkowski spacetimes are maximal invariant central extensions of the superpoint.
- The process uncovers the full brane content of string/M-theory.
- It establishes a direct link between algebraic extensions and physical spacetime structures.

## Abstract

The "brane scan" classifies consistent Green--Schwarz strings and membranes in terms of the invariant cocycles on super-Minkowski spacetimes. The "brane bouquet" generalizes this by consecutively forming the invariant higher central extensions induced by these cocycles, which yields the complete brane content of string/M-theory, including the D-branes and the M5-brane, as well as the various duality relations between these. This raises the question whether the super-Minkowski spacetimes themselves arise as maximal invariant central extensions. Here we prove that they do. Starting from the simplest possible super-Minkowski spacetime, the superpoint, which has no Lorentz structure and no spinorial structure, we give a systematic process of repeated "maximal invariant central extensions", and show that it discovers the super-Minkowski spacetimes that contain superstrings, culminating in the 10- and 11-dimensional super-Minkowski spacetimes of string/M-theory and leading directly to the brane bouquet.