Infinite conformal symmetry of critical fluctuations in two dimensions

A. A. Belavin, A. M. Polyakov, A. B. Zamolodchikov

Research output: Contribution to journalArticlepeer-review

296 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)763-774
Number of pages12
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Mar 1984

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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


Dive into the research topics of 'Infinite conformal symmetry of critical fluctuations in two dimensions'. Together they form a unique fingerprint.

Cite this