ar X iv : h ep - p h / 96 09 26 9 v 1 5 S ep 1 99 6 Electric - Magnetic Duality and the Heavy Quark Potential

We use the assumption of electric-magnetic duality to express the heavy quark potential in QCD in terms of a Wilson Loop W eff (Γ) determined by the dynamics of a dual theory which is weakly coupled at long distances. The classical approximation gives the leading contribution to W eff (Γ) and yields a velocity dependent heavy quark potential which for large R becomes linear in R, and which for small R approaches lowest order perturbative QCD. The corresponding long distance interaction between color magnetic monopoles is governed by a Yukawa potential. As a consequence the magnetic interaction between the color magnetic moments of the quarks is exponentially damped. The semi-classical corrections to W eff (Γ) due to fluctuations of the classical flux tube should lead to an effective string theory free from the conformal anomaly.