Aspects of mass gap, confinement and N=2 structure in 4-D Yang-Mills theory

TL;DR

This paper introduces new variables in 4D SU(N) Yang-Mills theory, revealing effective supersymmetric structures that could shed light on the confinement mechanism in pure Yang-Mills theory.

Contribution

It develops an effective field theory with emergent supersymmetry by summing over classical solutions, linking N=2 supersymmetry and Parisi-Sourlas reduction to confinement.

Findings

Effective theory exhibits N=2 supersymmetry in instanton approximation

Summation over solutions leads to Parisi-Sourlas supersymmetry

Mass terms break supersymmetry explicitly, suggesting a confinement mechanism

Abstract

We introduce new variables in four dimensional SU(N) Yang-Mills theory. These variables emerge when we sum the path integral over classical solutions and represent the summation as an integral over appropriate degrees of freedom. In this way we get an effective field theory with SU(N)$\times$SU(N) gauge symmetry. In the instanton approximation our effective theory has in addition a N=2 supersymmetry, and when we sum over all possible solutions we find a Parisi-Sourlas supersymmetry. These extra symmetries can then be broken explicitly by a SU(N) invariant and power counting renormalizable mass term. Our results suggest that the confinement mechanism which has been recently identified in the N=2 supersymmetric Yang-Mills theory might also help to understand color confinement in ordinary, pure Yang-Mills theory. In particular, there appears to be an intimate relationship between the N=2 supersymmetry approach to confinement and the Parisi-Sourlas dimensional reduction.