Continuum QCD2 In Terms of Discrete Random Surfaces with Local Weights

  • Ivan K. Kostov
Part of the NATO ASI Series book series (NSSB, volume 328)


The 1/N expansion of pure U(N) gauge theory on a two-dimensional manifold M is reformulated as the topological expansion of a special model of random surfaces defined on a lattice L covering M. The random surfaces represent branched coverings of L. The Boltzmann weight of each surface is exp[-area] times a product of local factors associated with the branch points. The 1/N corrections are produced by surfaces with higher topology as well as by contact interactions due to microscopic tubes, trousers, handles, etc. The continuum limit of this model is the limit of infinitely dense covering lattice L. The construction generalizes trivially to D > 2 where it describes the strong coupling phase of the lattice gauge theory. A possible integration measure in the space of continuous surfaces is suggested.


Gauge Theory Partition Function Branch Point Wilson Loop Continuum Limit 
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  1. [1]
    G. ’t Hooft, Nucl. Phys. B72 (1974) 461.ADSCrossRefGoogle Scholar
  2. [2]
    K. Wilson, Phys. Rev. D10 (1974) 2445; A.M. Polyakov, unpublished.ADSGoogle Scholar
  3. [3]
    Yu. M. Makeenko and A. A. Migdal, Nucl. Phys. B188 (1981) 269, A. A. Migdal, Phys. Rev. 102 (1983) 201.MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    V. Kazakov and I. Kostov, Nucl. Phys. B176 (1980) 199; V. Kazakov, Nucl. Phys. B179 (1981) 283.MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    B. Durhuus, J. Fröhlich and T. Jonsson, Nucl. Phys. B225 (1983) 185; Nucl. Phys. B240 (1984) 453.ADSCrossRefGoogle Scholar
  6. [6]
    D. Weingarten, Phys. Lett. 90B (1980) 285.ADSGoogle Scholar
  7. [7]
    V. Kazakov, Phys. Lett. 128B (1983) 316, JETP (Russian edition) 85 (1983) 1887.ADSGoogle Scholar
  8. [8]
    I. Rostov, Phys. Lett. 138B (1984) 191, 147B (1984) 445.ADSGoogle Scholar
  9. [9]
    K.H. O’Brien and J.-B. Zuber, Nucl. Phys. B253 (1985) 621, Phys. Lett. 144B (1984) 407.ADSCrossRefGoogle Scholar
  10. [10]
    D. Gross and E. Witten, Phys. Rev. D21 (1980) 446; S. Wadia, Chicago preprint EFI 80/15, unpublished.ADSGoogle Scholar
  11. [11]
    N.S. Manton, Phys. Lett. 96B (1980) 328; P. Menotti and E. Onofri, Nucl. Phys. B190 (1984) 288; C.B. Lang, P. Salomonson and B.S. Skagerstam, Phys. Lett. 107B (1981) 211, Nucl. Phys. B190 (1981) 337.MathSciNetADSGoogle Scholar
  12. [12]
    P. Rossi, Ann. Phys. 132 (1981) 463.ADSCrossRefGoogle Scholar
  13. [13]
    I. Rostov, Nucl. Phys. B265 (1986) 223.ADSGoogle Scholar
  14. [14]
    B. Rusakov, Mod. Phys. Lett. A5 (1990) 693.MathSciNetADSGoogle Scholar
  15. [15]
    D. Gross, Princeton preprint PUPT-1356, hep-th/9212149.Google Scholar
  16. [16]
    D. Gross and W. Taylor IV, preprints PUPT-1376 hep-th/9301068 and PUPT-1382 hep-th/9303046.Google Scholar
  17. [17]
    M. Douglas, Preprint RU-93-13 (NSF-ITP-93-39); A. D’Adda, M. Caselle, L. Magnea and S. Panzeri, Preprint hep-th 9304015; J. Minahan and A. Polychronakos, hep-th/9303153.Google Scholar
  18. [18]
    M. Douglas and V. Razakov, preprint LPTENS-93/20.Google Scholar
  19. [19]
    A. Polyakov, Phys. Lett. B (103) 207.Google Scholar
  20. [20]
    A. Polyakov, preprint PUPT-1394, April 1993.Google Scholar
  21. [21]
    J.-M. Drouffe and J.-B. Zuber, Phys. Rep. 102, Nos. 1, 2 (1983) 1-119, section 4.Google Scholar
  22. [22]
    E. Brézin and D. Gross, Phys. Lett. 97B (1980) 120.ADSGoogle Scholar
  23. [23]
    A.A. Migdal, unpublished (1978); D. Förster, Phys. Lett. 87B (1979) 87; T. Eguchi, Phys. Lett. 87B (1979) 91.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Ivan K. Kostov
    • 1
  1. 1.Service de Physique Théorique CE-SaclayGif-Sur-YvetteFrance

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