THE PARISI–SOURLAS MECHANISM IN YANG–MILLS THEORY?

Abstract

The Parisi–Sourlas mechanism is exhibited in pure Yang–Mills theory. Using the new scalar degrees of freedom derived from the nonlinear gauge condition, we show that the nonperturbative 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 [Formula: see text] is unchanged. This leads to dimensional reduction proving the equivalence of the nonperturbative sector of Yang–Mills theory to a 2D O(1, 3) sigma model.