Yang-Mills by dimensionally reducing Chern-Simons

TL;DR

This paper derives the standard Yang-Mills action in various dimensions through dimensional reduction from a Chern-Simons-like action, revealing a geometric interpretation involving auxiliary gauge fields for extra dimensions.

Contribution

It introduces a novel derivation of Yang-Mills theory from higher-dimensional Chern-Simons actions, linking auxiliary fields to extra-dimensional gauge symmetries.

Findings

Yang-Mills action obtained from Chern-Simons reduction

Auxiliary tensor field interpreted as gauge field for extra dimensions

Connects higher-dimensional geometry with gauge theories

Abstract

We derive the usual first-order form of the Yang-Mills action in arbitrary dimensions by dimensional reduction from a Chern-Simons-like action. The antisymmetric tensor auxiliary field of the first-order action appears as a gauge field for the extra dimensions. The higher-dimensional geometry was introduced in our previous paper by adding dimensions "dual" to spin, as suggested by the superstring's affine Lie algebra.