M-theory preons cannot arise by quotients

TL;DR

This paper proves that M-theory preons, solutions with 31 supersymmetries, cannot be obtained as quotients of maximally supersymmetric solutions, resolving a key question in eleven-dimensional supergravity.

Contribution

It demonstrates that no quotients of maximally supersymmetric solutions can produce M-theory preons, completing the classification of such solutions.

Findings

No quotients of maximally supersymmetric solutions yield preons.

The problem reduces to classifying cyclic group quotients in the exponential map image.

Completes the partial classification of relevant quotients.

Abstract

M-theory preons -- solutions of eleven-dimensional supergravity preserving 31 supersymmetries -- have recently been shown to be locally maximally supersymmetric. This implies that if preons exist they are quotients of maximally supersymmetric solutions. In this paper we show that no such quotients exist. This is achieved by reducing the problem to quotients by cyclic groups in the image of the exponential map, for which there already exists a partial classification, which is completed in the present paper.