A Short Introduction to Conformal Invariance

  • Malte HenkelEmail author
  • Dragi Karevski
Part of the Lecture Notes in Physics book series (LNP, volume 853)


An easily readable introduction to the main concepts and techniques of conformal invariance is provided. Starting from the global scale-invariance at a critical point, it is argued, through the local conformal Ward identities, that under mild conditions an extension to a local form of scale-invariance, namely conformally invariance, is in general possible. In two space dimensions, the particular role of the infinite-dimensional Lie algebra of conformal transformations is outlined and the main concepts, namely those of a primary scaling operator, the conformal energy-momentum tensor, the Virasoro algebra and the central charge and the main facts of their unitary and/or minimal representations will be presented. Some simple applications for the explicit calculation of two-point functions will be given. The free boson will be used as a paradigmatic illustration and we shall close with an outline of surface critical phenomena and their description in terms of boundary conformal field-theory.


Partition Function Vertex Operator Conformal Transformation Conformal Invariance Operator Product Expansion 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.GPS—DP2M—IJL (CNRS UMR 7198)Université de Lorraine NancyVandœuvre-lès-Nancy CedexFrance

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