Oriented Matroid Theory as a Mathematical Framework for M-Theory

TL;DR

This paper proposes using oriented matroid theory as a mathematical framework for M-theory, highlighting duality and introducing a new action for extended systems that unifies p-branes and their duals.

Contribution

It introduces a novel application of oriented matroid theory to M-theory, providing a new formalism based on the Farkas property and duality symmetry.

Findings

A new type of action for extended systems combining p-branes and dual p-branes.

Oriented matroid theory offers a potential mathematical foundation for M-theory.

Duality symmetry is central to the proposed formalism.

Abstract

We claim that $M$(atroid) theory may provide a mathematical framework for an underlying description of $M$-theory. Duality is the key symmetry which motivates our proposal. The definition of an oriented matroid in terms of the Farkas property plays a central role in our formalism. We outline how this definition may be carried over $M$-theory. As a consequence of our analysis we find a new type of action for extended systems which combines dually the $p$-brane and its dual $p^{\perp}$-brane.