Time exponentiation of a Wilson loop for Yang-Mills theories in 2 + ϵ dimensions Original Research Article

A rectangular Wilson loop centered at the origin, with sides parallel to space and time directions and length 2L and 2T respectively, is perturbatively evaluated O(g4) in the Feynman gauge for the Yang-Mills theory in 1 + (D − 1) dimensions. When D > 2, there is a dependence on the dimensionless ratio L/T, besides the area. In the limit T → ∞, keeping D > 2, the leading expression of the loop involves only the Casimir constant CF of the fundamental representation and is thereby in agreement with the expected Abelian-like time exponentiation (ALTE). At D = 2 the result depends also on CA, the Casimir constant of the adjoint representation and a pure area law behaviour is recovered, but no agreement with ALTE in the limit T → ∞. Consequences of these results concerning two- and higher-dimensional gauge theories are pointed out.