Journal of Statistical Physics

, Volume 34, Issue 5–6, pp 763–774 | Cite as

Infinite conformal symmetry of critical fluctuations in two dimensions

  • A. A. Belavin
  • A. M. Polyakov
  • A. B. Zamolodchikov


We study the massless quantum field theories describing the critical points in two dimensional statistical systems. These theories are invariant with respect to the infinite dimensional group of conformal (analytic) transformations. It is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the Virasoro algebra. Exactly solvable theories associated with degenerate representations are analized. In these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations.

Key words

Second order phase transitions two-dimensional systems operator algebra conformal symmetry Vivasoro algebra Kac formula 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Z. Patashinsky and V. L. Pokrovsky,Fluctuational Theory of Phase Transitions (Nauka, Moscow, 1982).Google Scholar
  2. 2.
    A. M. Polyakov,Zh. Eksp. Teor. Fiz. 66:23 (1974).Google Scholar
  3. 3.
    K. G. Wilson,Phys. Rev. 179:1499 (1969).Google Scholar
  4. 4.
    V. G. Kac,Lecture Notes in Physics 94:441 (1979).Google Scholar
  5. 5.
    S. Mandelstam,Phys. Rep. 12C:1441 (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • A. A. Belavin
    • 1
  • A. M. Polyakov
    • 1
  • A. B. Zamolodchikov
    • 1
  1. 1.Landau Institute for Theoretical PhysicsAcademy of Sciences of the USSRMoscowUSSR

Personalised recommendations