Maximal Supersymmetry in Eleven-Dimensional Supergravity Revisited and Chirotopes

TL;DR

This paper explores the role of chirotopes in eleven-dimensional supergravity, proposing that they could lead to new solutions and offering a novel mathematical perspective on maximal supersymmetry.

Contribution

It introduces the application of oriented matroid theory and chirotopes to analyze and potentially discover new solutions in higher-dimensional supergravity theories.

Findings

Chirotopes may yield new supergravity solutions.

Oriented matroid theory offers a novel framework for supersymmetry analysis.

Potential extension of solutions to higher-dimensional theories.

Abstract

We analyze maximal supersymmetry in eleven-dimensional supergravity from the point of view of the oriented matroid theory. The mathematical key tools in our discussion are the Englert solution and the chirotope concept. We argue that chirotopes may provide other solutions not only for eleven-dimensional supergravity but for any higher dimensional supergravity theory.