Four Dimensional Yang - Mills Theory in Local Gauge Invariant Variables

TL;DR

This paper introduces a method to reformulate 4D SU(N) Yang-Mills theory using only local gauge invariant variables, revealing a close similarity to R^2-gravity for N=2.

Contribution

It presents a novel approach to express Yang-Mills theory solely with gauge invariant variables, simplifying the analysis and drawing parallels to gravity theories.

Findings

For N=2, the formulation resembles R^2-gravity.

The method provides a gauge invariant description of 4D Yang-Mills.

Potential connections to gravity theories are explored.

Abstract

It is presented the general method that allows to formulate 4D $SU(N)$ Yang - Mills theory in terms of only local gauge invariant variables. For the case N=2, that is discussed in details, this gauge invariant formulation appears to be very similar to $ R^2 $-gravity.