Time exponentiation of a Wilson loop for Yang-Mills theories in 2+εdimensions

Abstract

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 $\mathcal{O}(g^4)$ in Feynman gauge for 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 $T\to \infty$, keeping $D>2$, the leading expression of the loop involves only the Casimir constant $C_F$ 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 $C_A$, the Casimir constant of the adjoint representation and a pure area law behavior is recovered, but no agreement with ALTE in the limit $T\to \infty$. Consequences of these results concerning two and higher-dimensional gauge theories are pointed out.

RevTex, 28 pages, two figure files included

References in corpus (1)

• Two-Dimensional QCD in the Wu-Mandelstam-Leibbrandt Prescription

Cited by in corpus (6)

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• Two-dimensional Yang-Mills theory: perturbative and instanton contributions, and its relation to QCD in higher dimensions
• Discontinuous behavior of perturbative Yang-Mills theories in the limit of dimensions D->2
• Wilson Loops in Two-Dimensional Yang-Mills Theories