Gauge Theories and Non-Commutative Geometry

TL;DR

This paper demonstrates how a classical SU(N) Yang-Mills theory in d dimensions can be reformulated in a higher-dimensional space with non-commutative geometry, revealing new geometric structures.

Contribution

It introduces a novel formulation of Yang-Mills theories in higher dimensions incorporating non-commutative geometry, expanding the understanding of gauge theories.

Findings

Yang-Mills theory reformulated in d+2 dimensions

Extra dimensions exhibit non-commutative geometric structure

Potential implications for quantum field theory and string theory

Abstract

It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.