The Parisi-Sourlas Mechanism in Yang-Mills Theory?

TL;DR

This paper demonstrates that the non-perturbative sector of pure Yang-Mills theory exhibits the Parisi-Sourlas mechanism, leading to a dimensional reduction to a 2D O(1,3) sigma model through supersymmetry invariance.

Contribution

It reveals the Parisi-Sourlas mechanism in Yang-Mills theory and establishes a non-perturbative equivalence to a 2D sigma model via supersymmetry.

Findings

Non-perturbative Yang-Mills maps to a 4D O(1,3) sigma model in a random field.

Leading term exhibits supersymmetry invariance, enabling dimensional reduction.

Non-perturbative sector is equivalent to a 2D O(1,3) sigma model.

Abstract

The Parisi-Sourlas mechanism is exhibited in pure Yang-Mills theory. Using the new scalar degrees of freedom derived from the non-linear gauge condition, we show that the non-perturbative sector of Yang-Mills theory is equivalent to a 4D O(1,3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where (x^{2}+\thetabar\theta) is unchanged. This leads to dimensional reduction proving the equivalence of the non-perturbative sector of Yang-Mills theory to a 2D O(1,3) sigma model.