A Gauge-Independent Mechanism for Confinement and Mass Gap: Part I -- The General Framework

TL;DR

This paper introduces a gauge-independent approach to understanding confinement and the mass gap in Yang-Mills theory, using an exact transformation applicable at all couplings, with implications for the continuum limit.

Contribution

It presents a novel, exact transformation of lattice Yang-Mills theory that explains confinement without gauge dependence, applicable across all coupling regimes.

Findings

Proposes a gauge-independent mechanism for Wilson loop area-law behavior.

Framework valid for all couplings, including the continuum limit.

Provides conjectures on the physical origin of confinement in weak coupling.

Abstract

We propose a gauge-independent mechanism for the area-law behavior of Wilson loop expectation values in terms of worldsheets spanning Wilson loops interacting with the spin foams that contribute to the vacuum partition function. The method uses an exact transformation of lattice-regularized Yang-Mills theory that is valid for all couplings. Within this framework, some natural conjectures can be made as to what physical mechanism enforces the confinement property in the continuum (weak coupling) limit. Details for the SU(2) case in three dimensions are provided in a companion paper.