Baker, M. and Ball, J. S. and Brambilla, N. and Prosperi, G. M. and Zachariasen, F. (1996) Confinement: Understanding the relation between the Wilson loop and dual theories of long distance YangMills theory. Physical Review D, 54 (4). pp. 28292844. ISSN 24700010. https://resolver.caltech.edu/CaltechAUTHORS:BAKprd96

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Abstract
In this paper we express the velocitydependent, spindependent heavy quark potential Vqq̅ in QCD in terms of a Wilson loop W(Γ) determined by pure YangMills theory. We use an effective dual theory of longdistance YangMills theory to calculate W(Γ) for large loops, i.e., for loops of size R>RFT. [RFT is the flux tube radius, fixed by the value of the Higgs (monopole) mass of the dual theory, which is a concrete realization of the Mandelstam't Hooft dual superconductor mechanism of confinement.] We replace W(Γ) by Weff(Γ), given by a functional integral over the dual variables, which for R>RFT can be evaluated by a semiclassical expansion, since the dual theory is weakly coupled at these distances. The classical approximation gives the leading contribution to Weff(Γ) and yields a velocitydependent heavy quark potential that for large R becomes linear in R, and that for small R approaches lowestorder perturbative QCD. This latter fact means that these results should remain applicable down to distances where radiative corrections giving rise to a running coupling constant become important. The spin dependence of the potential at long range as well as at short range reflects the vector coupling of quarks in QCD combined with the dual treatment of longdistance YangMills theory. The methods developed here should be applicable to any realization of the dual superconductor mechanism. They give an expression determining Weff(Γ) independent of the classical approximation, but semiclassical corrections due to fluctuations of the flux tube are not worked out in this paper. Taking these into account should lead to an effective string theory free from the conformal anomaly.
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Additional Information:  ©1996 The American Physical Society Received 4 March 1996 One of us (M.B) would like to thank M. Polikarpov and L. Yaffe for enlightening conversations. The work of M.B. was supported in part by the U.S. Department of Energy under Grant No. DOE/ER/40614. The work of F.Z. was supported in part by the U.S. Department of Energy under Grant No. DEFG0392ER40701. Erratum: M. Baker, J. S. Ball, N. Brambilla, G. M. Prosperi, and F. Zachariasen, Erratum: Confinement: Understanding the relation between the Wilson loop and dual theories of long distance YangMills theory [Phys. Rev. D 54, 2829 (1996)], Phys. Rev. D 56, 2475 (1997).  
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Deposited On:  22 Mar 2006  
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