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.

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