Realization of dimensional reduction at high temperature

  • T. Reisz


Renormalizable four-dimensional field theories reduce at high temperature to effective three-dimensional field models with generically nonlocal interactions induced by the thermal degrees of freedom. Reduction to a local and renormalizable effective model is analyzed here for the example ofSU(N c ) lattice gauge theory by means of perturbation theory. The infrared problems are cured by applying the coupled large volume and small coupling expansion. ForSU(2) it is shown to the lower orders in this expansion that in the temperature rangeT≧3T c dimensional reduction applies, where we consider the following observables: thermal Polyakov line correlations, out of which the interquark potential is derived, and spatial Wilson loops. We also propose an alternative description, in which the effective theory is a gauge theory that lives on a lattice with one time slice and a least number of effective vertices.


Gauge Theory Dimensional Reduction Wilson Loop Time Slice Lattice Gauge Theory 
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  1. 1.
    R.J. Rivers: Path integral methods in quantum field theory. Cambridge: Cambridge University Press 1987Google Scholar
  2. 2.
    J.I. Kapusta: Finite temperature field theory. Cambridge: Cambridge University Press 1989Google Scholar
  3. 3.
    N.P. Landsman: Nucl. Phys. B 322 (1989) 498Google Scholar
  4. 4.
    R. Alvarez-Estrada: Fortschr. Phys. 36 (1988) 163Google Scholar
  5. 5.
    J. Ambjørn: Commun. Math. Phys. 67 (1979) 109Google Scholar
  6. 6.
    T. Appelquist, J. Carazzone: Phys. Rev. D 11 (1975) 2856; T. Appelquist, R.D. Pisarski: Phys. Rev. D23 (1981) 2305Google Scholar
  7. 7.
    W.E. Caswell, A.D. Kennedy: Phys. Rev. D 28 (1983) 3073Google Scholar
  8. 8.
    S. Nadkarni: Phys. Rev. D 27 (1983) 917Google Scholar
  9. 9.
    S. Nadkarni: Phys. Rev. D 38 (1988) 3287Google Scholar
  10. 10.
    A.N. Jourjine: Ann. Phys. 155 (1984) 305Google Scholar
  11. 11.
    C. Curci, P. Menotti, G. Paffuti: Z. Phys. C — Particles and Fields 26 (1985) 549Google Scholar
  12. 12.
    T. Reisz: J. Math. Phys. 32 (1991) 515Google Scholar
  13. 13.
    B. Petersson, T. Reisz: Nucl. Phys. B 353 (1991) 757Google Scholar
  14. 14.
    T. Reisz: Commun. Math. Phys. 117 (1988) 79Google Scholar
  15. 15.
    A. Irbäck et al.: Nucl. Phys. B 363 (1991) 34Google Scholar
  16. 16.
    T. Reisz: Commun. Math. Phys. 116 (1988) 573Google Scholar
  17. 17.
    A. Coste, A. Gonzalez-Arroyo, J. Jurkiewicz, C.P. Korthals-Altes. Nucl. Phys. B 262 (1985) 67Google Scholar
  18. 18.
    P. Weisz: Nucl. Phys. B 212 (1983) 1Google Scholar
  19. 19.
    U. Heller, F. Karsch: Nucl. Phys. B 251 [FS13] (1985) 254Google Scholar
  20. 20.
    V.S. Dotsenko, S.N. Vergeles: Nucl. Phys. B 169 (1980) 527Google Scholar
  21. 21.
    C. Borgs, E. Seiler: Nucl. Phys. B 215 [FS] (1983) 125Google Scholar
  22. 22.
    C. Borgs, E. Seiler: Commun. Math Phys. 91 (1983) 329Google Scholar
  23. 23.
    T. Reisz: Nucl. Phys. B 318 (1989) 417Google Scholar
  24. 24.
    H. Matsumoto, I. Ojima, H. Umezawa: Ann. Phys. 152 (1984) 348Google Scholar
  25. 25.
    N.P. Landsman, Ch.G. van Weert: Phys. Rep. 145 (1987) 141Google Scholar
  26. 26.
    S. Nadkarni: Phys. Rev. D 33 (1986) 3738Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • T. Reisz
    • 1
  1. 1.Fakultät für PhysikUniversität BielefeldBielefeld 1Federal Republic of Germany

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