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Properties of the Confining Force

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An Introduction to the Confinement Problem

Part of the book series: Lecture Notes in Physics ((LNP,volume 821))

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Abstract

Any fully satisfactory theory of confinement ought to explain the following features of the confining force, for which there is strong theoretical and/or numerical support:

  1. 1.

    asymptotic linearity of the static potential;

  2. 2.

    Casimir scaling of string tensions at intermediate distance scales;

  3. 3.

    N-ality dependence of asymptotic string tensions;

  4. 4.

    evidence of quantum string-like behavior: roughening and the Lüscher term.

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Notes

  1. 1.

    It should be noted that the calculation on which this figure is based uses a method which creates metastable flux tubes, which are then allowed to propagate for a relatively short Euclidean time interval. This procedure is insensitive to the string-breaking process, and hence one can only calculate the string tension of the metastable states.

  2. 2.

    To add to the “Casimir” confusion, the Lüscher term is known to string theorists as the “Casimir energy.”

References

  1. Bachas, C.: Convexity of the Quarkonium Potential. Phys. Rev. D 33, 2723–2725 (1986)

    Article  ADS  Google Scholar 

  2. Bali. G.: QCD forces and heavy quark bound states. Phys. Rept. 343, 1–136 (2001) [arXiv: hep-ph/0001312]

    Google Scholar 

  3. Ambjorn, J., Olesen, P., Peterson, C.: Stochastic confinement and dimensional reduction (I): four-dimensional SU(2) lattice gauge theory. Nucl. Phys. B 240, 189–212; 533–542 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  4. Olesen, P.: Confinement and random fluxes. Nucl. Phys. B 200(FS4), 381–390 (1982)

    Article  ADS  Google Scholar 

  5. Greensite, J.: Calculation of the Yang–Mills vacuum wave functional. Nucl. Phys. B 158, 469–496 (1979)

    Google Scholar 

  6. Greensite, J.: Large scale vacuum structure and new calculational techniques in lattice SU(N) gauge theory. Nucl. Phys. B 166, 113–124 (1980)

    Google Scholar 

  7. Bali, G.: Casimir scaling of SU(3) static potentials. Phys. Rev. D 62, 114503-1–114503-11 (2000) [arXiv: hep-lat/0006022]

    Google Scholar 

  8. Del Debbio, L., Faber, M., Greensite, J., Olejník, Š.: Casimir scaling versus Abelian dominance in QCD string formation. Phys. Rev. D 53, 5891–5897 (1996) [arXiv: hep-lat/9510028]

    Google Scholar 

  9. Del Debbio, L., Faber, M., Greensite, J., Olejník, Š.: Some cautionary remarks on Abelian projection and Abelian dominance. Nucl. Phys. Proc. Suppl. 53, 141–147 (1997) [arXiv: hep-lat/9607053]

    Google Scholar 

  10. de Forcrand, P., Kratochvila, S.: Observing string breaking with Wilson loops. Nucl. Phys. B 671, 103–132 (2003) [arXiv: hep-lat/0209094]

    Google Scholar 

  11. Lüscher, M., Weisz, P.: Quark confinement and the bosonic string. JHEP 07, 049-1–049-18 (2002) [arXiv: hep-lat/0207003]

    Google Scholar 

  12. Lüscher, M.: Symmetry breaking aspects of the roughening transition in gauge theories. Nucl. Phys. B 180(FS2), 317–329 (1981)

    Article  ADS  Google Scholar 

  13. Alvarez, O.: The static potential in string models. Phys. Rev. D 24, 440–449 (1981)

    Article  ADS  Google Scholar 

  14. Lüscher, M., Münster, G., Weisz, P.: How thick are chromoelectric flux tubes? Nucl. Phys. B 180(FS2), 1–12 (1981)

    Google Scholar 

  15. Hasenfratz, A., Hasenfratz, E., Hasenfratz, P.: Generalized roughening transition and its effect on the string tension. Nucl. Phys. B 180(FS2), 353–367 (1981)

    Google Scholar 

  16. Juge, K.J., Kuti, J., Morningstar, C.: QCD string formation and the Casimir energy [arXiv: hep-lat/0401032]

    Google Scholar 

  17. Bornyakov, V.G., Kovalenko, A.V., Polikarpov, M.I., Sigaev, D.A.: Confining string and P vortices in the indirect Z(2) projection of SU(2) lattice gauge theory. Nucl. Phys. Proc. Suppl. 119, 739–741 (2003) [arXiv:hep-lat/0209029]

    Google Scholar 

  18. Kuti, J.: Lattice QCD and string theory. PoS LAT 2005, 1–22 (2006) [arXiv:hep-lat/0511023]

    Google Scholar 

  19. Athenodorou, A., Bringoltz, B., Teper, M.: The closed string spectrum of SU(N) gauge theories in 2 + 1 dimensions. Phys. Lett. B 656, 132–140 (2007) [arXiv:0709.0693 [hep-lat]]

    Google Scholar 

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Correspondence to Jeff Greensite .

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Greensite, J. (2010). Properties of the Confining Force. In: An Introduction to the Confinement Problem. Lecture Notes in Physics, vol 821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14382-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-14382-3_5

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