Fractal Wilson loop and confinement in non-compact gauge field theory

Abstract

We make a new proposal to explain why quarks and gluons confine. We study SU(2) gauge theory in non-compact formulation. We suggest a new observable 〈 F p 〉, a fractal Wilson loop, which in the classical continuum limit coincides with the standard Wilson loop. The new observable is expressed in terms of an ordered surface- and line-integral, corresponding to a fractal geometry. To lowest order in the strong coupling expansion 〈 F p 〉 is gauge invariant and yields an area law, i.e., confinement. Like the standard Wilson loop, 〈 F p 〉 allows an interpretation in terms of a static heavy quark potential.