$q\bar q$ interaction in light-cone gauge formulations of Yang-Mills theory in 1+1 dimensions

TL;DR

This paper compares two light-cone gauge formulations of 1+1 dimensional Yang-Mills theory by evaluating Wilson loops, revealing differences in their dependence on area, Casimir operators, and the ratio of rectangle sides, with implications for understanding quark interactions.

Contribution

It provides a perturbative analysis of Wilson loops in two light-cone gauge formulations, highlighting differences in their dependence on geometric and group-theoretic factors.

Findings

Instantaneous formulation shows Abelian-like area exponentiation.

Causal formulation depends on area and the ratio of sides, also involving $C_A$.

Area law is recovered as $T o fty$, but $C_A$ dependence persists.

Abstract

A rectangular Wilson loop with sides parallel to space and time directions is perturbatively evaluated in two light-cone gauge formulations of Yang-Mills theory in 1+1 dimensions, with ``instantaneous'' and ``causal'' interactions between static quarks. In the instantaneous formulation we get Abelian-like exponentiation of the area in terms of $C_F$. In the ``causal'' formulation the loop depends not only on the area, but also on the dimensionless ratio $\beta = {L \over T}$, $2L$ and $2T$ being the lengths of the rectangular sides. Besides it also exhibits dependence on $C_A$. In the limit $T \to \infty$ the area law is recovered, but dependence on $C_A$ survives. Consequences of these results are pointed out.