Chapter

Conformal field theory

Hidetoshi Nishimori and Gerardo Ortiz

in Elements of Phase Transitions and Critical Phenomena

Published in print December 2010 | ISBN: 9780199577224
Published online January 2011 | e-ISBN: 9780191722943 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199577224.003.0006

Series: Oxford Graduate Texts

Conformal field theory

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The present chapter is an introductory account of the basic concepts and important consequences of conformal symmetry, i.e. the invariance under local scale transformations, in field theories characterizing critical behaviour. The goal is to catalogue universality classes as a list of possible values of critical exponents and to find restrictions on the functional forms of correlation functions, which satisfy conformal Ward identities. From a mathematics standpoint, conformal symmetry applies to continuum theories, and therefore its obvious application to critical phenomena is formulated in the language of field theory. The energy-momentum tensor plays a fundamental role in defining the conformal generators that satisfy the Virasoro algebra, and any conformal field theory is characterized by the central charge a number that is important to classify critical field theories. One of the most remarkable applications of conformal field theory is found in the analysis of finite-size effects.

Keywords: local scale transformation; conformal invariance; universality class; correlation function; primary operators; Ward identity; Virasoro algebra; central charge

Chapter.  12805 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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