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Effective Lagrangian for the Polyakov line on a lattice

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Abstract

We formulate a method for computing the effective Lagrangian of the Polyakov line on the lattice. Using mean field approximation we calculate the effective potential for high temperatures. The result agrees with recent lattice simulations. We reveal a new type of ultraviolet divergence (coming from longitudinal gluons) which dominates the effective potential and explains the discrepancy of the lattice simulations and standard perturbative calculations performed in covariant gauges.

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References

  1. A.M. Polyakov, Thermal properties of gauge fields and quark liberation, Phys. Lett. B 72 (1978) 477 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. L. Susskind, Lattice models of quark confinement at high temperature, Phys. Rev. D 20 (1979) 2610 [INSPIRE].

    ADS  Google Scholar 

  3. B. Svetitsky and L.G. Yaffe, Critical behavior at finite temperature confinement transitions, Nucl. Phys. B 210 (1982) 423 [INSPIRE].

    Article  ADS  Google Scholar 

  4. L.G. Yaffe and B. Svetitsky, First order phase transition in the SU(3) gauge theory at finite temperature, Phys. Rev. D 26 (1982) 963 [INSPIRE].

    ADS  Google Scholar 

  5. D. Diakonov, C. Gattringer and H.-P. Schadler, Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory, JHEP 08 (2012) 128 [arXiv:1205.4768] [INSPIRE].

    Article  ADS  Google Scholar 

  6. D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. N. Weiss, The effective potential for the order parameter of gauge theories at finite temperature, Phys. Rev. D 24 (1981) 475 [INSPIRE].

    ADS  Google Scholar 

  8. N. Weiss, The Wilson line in finite temperature gauge theories, Phys. Rev. D 25 (1982) 2667 [INSPIRE].

    ADS  Google Scholar 

  9. D. Diakonov and M. Oswald, Covariant derivative expansion of Yang-Mills effective action at high temperatures, Phys. Rev. D 68 (2003) 025012 [hep-ph/0303129] [INSPIRE].

    ADS  Google Scholar 

  10. D. Diakonov and M. Oswald, Gauge invariant effective action for the Polyakov line in the SU(N) Yang-Mills theory at high temperatures, Phys. Rev. D 70 (2004) 105016 [hep-ph/0403108] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. C. Gattringer and C.B. Lang, Quantum chromodynamics on the lattice, Lect. Notes Phys. 788 (2010) 1 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. H. Reinhardt and J. Heffner, The effective potential of the confinement order parameter in the Hamilton approach, Phys. Lett. B 718 (2012) 672 [arXiv:1210.1742] [INSPIRE].

    Article  ADS  Google Scholar 

  13. H. Reinhardt and J. Heffner, The effective potential of the confinement order parameter in the Hamiltonian approach, Phys. Rev. D 88 (2013) 045024 [arXiv:1304.2980] [INSPIRE].

    ADS  Google Scholar 

  14. D. Smith, A. Dumitru, R. Pisarski and L. von Smekal, Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues, Phys. Rev. D 88 (2013) 054020 [arXiv:1307.6339] [INSPIRE].

    ADS  Google Scholar 

  15. J.-M. Drouffe and J.-B. Zuber, Strong coupling and mean field methods in lattice gauge theories, Phys. Rept. 102 (1983) 1 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. C. Itzykson and J.M. Drouffe, Statistical field theory. Vol. 1: From Brownian motion to renormalization and lattice gauge theory, Cambridge University Press, Cambridge U.K. (1989) [INSPIRE].

  17. P. de Forcrand and D. Noth, Precision lattice calculation of SU(2) ’t Hooft loops, Phys. Rev. D 72 (2005) 114501 [hep-lat/0506005] [INSPIRE].

    ADS  Google Scholar 

  18. I. Yotsuyanagi, Continuum limit of the O(3) nonlinear Σ lattice model in three-dimensions, Phys. Lett. B 163 (1985) 207 [INSPIRE].

    Article  ADS  Google Scholar 

  19. O. Kaczmarek, F. Karsch, P. Petreczky and F. Zantow, Heavy quark anti-quark free energy and the renormalized Polyakov loop, Phys. Lett. B 543 (2002) 41 [hep-lat/0207002] [INSPIRE].

    Article  ADS  Google Scholar 

  20. A. Dumitru, Y. Hatta, J. Lenaghan, K. Orginos and R.D. Pisarski, Deconfining phase transition as a matrix model of renormalized Polyakov loops, Phys. Rev. D 70 (2004) 034511 [hep-th/0311223] [INSPIRE].

    ADS  Google Scholar 

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Authors and Affiliations

  1. Petersburg Nuclear Physics Institute, Kurchatov National Research Centre, Gatchina, St. Petersburg, 188300, Russia

    Dmitri Diakonov & Victor Petrov

  2. St. Petersburg Academic University, St. Petersburg, 194021, Russia

    Dmitri Diakonov

  3. Institute for Physics, Karl-Franzens-Universität Graz, Universitätsplatz 5, 8010, Graz, Austria

    Hans-Peter Schadler & Christof Gattringer

Authors
  1. Dmitri Diakonov
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  2. Victor Petrov
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  3. Hans-Peter Schadler
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  4. Christof Gattringer
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Corresponding author

Correspondence to Christof Gattringer.

Additional information

On December 26 2012 our esteemed colleague Dmitri Diakonov passed away untimely early. At that time he was working with one of us (V.P.) on a follow up project to a paper we had published in June of that year. This article is based on this cooperation and we dedicate it to the memory of our friend Dmitri Diakonov.

ArXiv ePrint: 1308.2328

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Diakonov, D., Petrov, V., Schadler, HP. et al. Effective Lagrangian for the Polyakov line on a lattice. J. High Energ. Phys. 2013, 207 (2013). https://doi.org/10.1007/JHEP11(2013)207

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  • DOI: https://doi.org/10.1007/JHEP11(2013)207

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