Orbifold Singularities, Lie Algebras of the Third Kind (LATKes), and Pure Yang-Mills with Matter

TL;DR

This paper introduces the unique Lie Algebra of the Third Kind (LATKe) derived from orbifold singularities, leading to a Yang-Mills theory that is both pure and matter-containing, with implications for vacuum selection.

Contribution

It identifies the unique LATKe structure from orbifold singularities, providing a novel algebraic foundation for Yang-Mills theories with matter.

Findings

LATKe has a 1-dimensional root space

Dynkin diagram of LATKe consists of one point

LATKe acts as a vacuum selection mechanism

Abstract

We discover the unique, simple Lie Algebra of the Third Kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a kind of Yang-Mills theory which simultaneously is pure and contains matter. The root space of the LATKe is 1-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism.