Theoretical and Mathematical Physics

, Volume 95, Issue 2, pp 604–625 | Cite as

On the continuum limit of the conformal matrix models

  • A. Mironov
  • S. Pakuliak


The double scaling limit of a new class of the multi-matrix models proposed in [1], which possess the W-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the paper [2] is proposed, the corresponding partition functions being compared. All calculations are demonstrated in full in the first non-trivial case of W(3)-constraints.


Partition Function Matrix Model Continuum Limit Universality Class Discrete Level 


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  1. [1]
    Marshakov A., Mironov A., Morozov A.// Phys. Lett. 1991. V. B265. P. 99.Google Scholar
  2. [2]
    Fukuma M., Kawai H., Nakayama, R.// Int. J. Mod. Phys. 1991. V. A6. P. 1385.Google Scholar
  3. [3]
    Kazakov V.// Phys. Lett. 1985. V. B159. P. 303.Google Scholar
  4. [4]
    David F.// Nucl. Phys. 1985. V. B257. P. 45.Google Scholar
  5. [5]
    Regge T.// Nuovo Cim. 1961. V. 19. P. 558.Google Scholar
  6. [6]
    Kazakov V.// Mod. Phys. Lett. 1989. V. A4. P. 2125.Google Scholar
  7. [7]
    Brézin E., Kazakov V.// Phys. Lett. 1990. V. B235. P. 144.Google Scholar
  8. [8]
    Douglas M., Shenker S.// Nucl. Phys. 1990. V. B335. P. 635.Google Scholar
  9. [9]
    Gross D., MigdalA.// Phys. Rev. Lett. 1990. V. 64. P. 127.Google Scholar
  10. [10]
    Gross D., Migdal A.// Nucl. Phys. 1990. V. B340. P. 333.Google Scholar
  11. [11]
    Brézin E., Douglas M., Kazakov V., Shenker S.// Phys. Lett. 1990. V. 237B. P. 43.Google Scholar
  12. [12]
    Crnković Č., Ginsparg P., Moore G.// Phys. Lett. 1990. 237B. P. 196.Google Scholar
  13. [13]
    Gross D., Migdal A.// Phys. Rev. Lett. 1990. V. 64. P. 717.Google Scholar
  14. [14]
    Douglas M.// Phys. Lett. 1990. V. B238. P. 179.Google Scholar
  15. [15]
    Dijkgraaf R., Verlinde H., Verlinde E.// Nucl. Phys. 1991. V. B348. P. 435.Google Scholar
  16. [16]
    Izergin A. G., Korepin V. E.// Nucl. Phys. 1982. V.B205. P. 401.Google Scholar
  17. [17]
    Gerasimov A. et al.// Nucl. Phys. 1991. V. B357. P. 565.Google Scholar
  18. [18]
    Mironov A., Morozov A.// Phys. Lett. 1990. V. 252B. P. 47.Google Scholar
  19. [19]
    Ambjørn J., Jurkiewicz J., Makeenko Yu.// Phys. Lett. 1990. V. 251B. P. 517.Google Scholar
  20. [20]
    Makeenko Yu. et al.// Nucl. Phys. P. 1991. V. B356. P. 574.Google Scholar
  21. [21]
    Gerasimov A. et al. Mod. Phys. Lett. 1991. V. A6. P. 3079.Google Scholar
  22. [22]
    Kharchev S. et al.// Nucl. Phys. 1991. V. 366B. P. 569.Google Scholar
  23. [23]
    Kharchev S. et al. Generalized Kontsevich model versus Toda hierarchy and discrete matrix models. Preprint FIAN/TD-03/92-ITEP-M-3/92, hepth@xxx/9203043Google Scholar
  24. [24]
    Gava E., Narain K.// Phys. Lett. 1991. V. B263. P. 213.Google Scholar
  25. [25]
    Marshakov A., Mironov A., Morozov A.// Mod. Phys. Lett. 1992. V. A7. P. 1345.Google Scholar
  26. [26]
    Kharchev S. et al. Conformal matrix models as an alternative to conventional multi-matrix models. Preprint FIAN/TD-09/92-ITEP-M-4/92, hepth@xxx/9208044.Google Scholar
  27. [27]
    Fateev V., Lukyanov S.// Int. J. Mod. Phys. 1988. V. A3. P. 507.Google Scholar
  28. [28]
    Feigin B., Frenkel E. Preprint MIT, 1992.Google Scholar
  29. [29]
    Ablowitz M. J., Kaup D. J., Newell A. C., Segur H.// Stud. Appl. Math. 1974. V. 53. P. 249.Google Scholar
  30. [30]
    Ueno K., Takasaki K// Adv. Studies in Pure Math. 1984. V. 4. P. 1.Google Scholar
  31. [31]
    See, for example,Morozov A.// Nucl Phys. 1991. V. 357B. P. 619.Google Scholar
  32. [32]
    Zamolodchikov A. B.// Teor. Mat. Fiz. 1985. V. 65. P. 347.Google Scholar
  33. [33]
    Fukuma M., Kawai H., Nakayama R.// Com. Math. Phys. 1992. V. 143. P. 371.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • A. Mironov
  • S. Pakuliak

There are no affiliations available

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