On the consistency of coset space dimensional reduction

TL;DR

This paper investigates the consistent reduction of higher-dimensional Yang-Mills theories over coset spaces, demonstrating that reducing the Lagrangian and equations of motion yields equivalent four-dimensional gauge theories, exemplifying a consistent truncation.

Contribution

It provides a systematic approach to achieve consistent coset space dimensional reduction for higher-dimensional Yang-Mills theories, ensuring equivalence of reduced Lagrangian and equations of motion.

Findings

Reduction yields equivalent four-dimensional gauge theories

Establishes a method for consistent truncation

Demonstrates the validity of the reduction approach

Abstract

In this letter we consider higher-dimensional Yang-Mills theories and examine their consistent coset space dimensional reduction. Utilizing a suitable ansatz and imposing a simple set of constraints we determine the four-dimensional gauge theory obtained from the reduction of both the higher-dimensional Lagrangian and the corresponding equations of motion. The two reductions yield equivalent results and hence they constitute an example of a consistent truncation.