Dimensionally Reduced Yang-Mills Theories in Noncommutative Geometry

TL;DR

This paper explores noncommutative geometries that lead to dimensionally reduced Yang-Mills theories, highlighting their structure as multiple copies of even-dimensional manifolds and discussing their relation to D-branes in string theory.

Contribution

It introduces a class of noncommutative geometries that produce dimensionally reduced Yang-Mills theories with a novel geometric interpretation.

Findings

Geometries describe multiple copies of even-dimensional manifolds

Connections to D-branes in string theory are discussed

Framework for noncommutative geometries in gauge theories

Abstract

We study a class of noncommutative geometries that give rise to dimensionally reduced Yang-Mills theories. The emerging geometries describe sets of copies of an even dimensional manifold. Similarities to the D-branes in string theory are discussed.