Recent Results in Two-Dimensional Conformal Field Theory

  • Andrea Cappelli§
Conference paper

Abstract

We shall discuss the methods of conformal field theory (CFT), which were first introduced in [1]; detailed applications to critical phenomena are described in De Vega’s talk and [2], applications to string theory are found in [3], in particular [4]. In two dimensions, analytic transformations zz′ = z′ (z) of the coordinate z = x° + ix 1, and anti-analytic ones of z = x° — ix 1 yield conformal rescalings of the euclidean metric. These transformations obey the Virasoro algebra, which is an infinite-dimensional algebra; this means that the associated Ward identities for correlations functions are local In some special cases, these reduce to a finite set of differential equations, whose solutions give correlations functions and scaling dimensions of fields. Therefore we do not speak of lagrangians in a specified model, but we assume some fields and their correlations functions as a definition of the field theory.

Keywords

Entropy Manifold Covariance Kato 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Andrea Cappelli§
    • 1
  1. 1.Service de Physique Théorique de SaclayInstitut de Recherche Fondamentale du Commissariat à l’Energie AtomiqueGif-sur-Yvette CedexFrance

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