Recently, a fractal Wilson loop <FP> has been suggested to yield for non-compact SU(2) gauge theory an area law in the strong-coupling regime, while the standard Wilson loop <WP> yields a perimeter law. Here we consider non-compact U(1) gauge theory, compute the fractal Wilson loop analytically, and obtain a perimeter law for all coupling. We find that <FP> and <WP> coincide.
Abelian color cycles: A new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory