Towards a solution of pure Yang-Mills theory in 3+1 dimensions

TL;DR

This paper explores an analytic approach to solving pure Yang-Mills theory in 3+1 dimensions using gauge-invariant variables and the large N limit, revealing parallels with 2+1 dimensions and insights from lattice simulations.

Contribution

It introduces a novel analytic framework employing gauge-invariant variables and the large N limit to study Yang-Mills theory in 3+1 dimensions, highlighting unexpected similarities with lower-dimensional cases.

Findings

Identifies parallels between 2+1 and 3+1 dimensional Yang-Mills theories.

Suggests the ground state wave-functional shares features across dimensions.

Notes numerical similarities in spectra from lattice simulations.

Abstract

We discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime. The approach is based on the use of local gauge invariant variables in the Schr\"odinger representation and the large $N$, planar limit. In particular, within this approach we point out unexpected parallels between pure Yang-Mills theory in 2+1 and 3+1 dimensions. The most important parallel shows up in the analysis of the ground state wave-functional especially in view of the numerical similarity of the existing large N lattice simulations of the spectra of 2+1 and 3+1 Yang Mills theories.