Infinite conformal symmetry of critical fluctuations in two dimensions

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

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296 Scopus citations

Abstract

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
Volume34
Issue number5-6
DOIs
StatePublished - Mar 1984

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

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

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