A Mathematical Introduction to Conformal Field Theory
The first part of this book gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. In particular, the conformal groups are determined and the appearan
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M. Schottenloher
A Mathematical Introduction to Conformal Field Theory Second Edition
Martin Schottenloher Mathematisches Institut Ludwig-Maximilians-Universit¨at M¨unchen Theresienstr. 39 80333 M¨unchen Germany [email protected]
Schottenloher, M. A Mathematical Introduction to Conformal Field Theory, Lect. Notes Phys. 759 (Springer, Berlin Heidelberg 2008), DOI 10.1007/978-3-540-68628-6
ISBN: 978-3-540-68625-5
e-ISBN: 978-3-540-68628-6
DOI 10.1007/978-3-540-68628-6 Lecture Notes in Physics ISSN: 0075-8450 Library of Congress Control Number: 2008928145 c 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar S.L., F. Steinen-Broo, Pau/Girona, Spain Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
To Barbara
Preface to the Second Edition
The second edition of these notes has been completely rewritten and substantially expanded with the intention not only to improve the use of the book as an introductory text to conformal field theory, but also to get in contact with some recent developments. In this way we take a number of remarks and contributions by readers of the first edition into consideration who appreciated the rather detailed and self-contained exposition in the first part of the notes but asked for more details for the second part. The enlarged edition also reflects experiences made in seminars on the subject. The interest in conformal field theory has grown during the last 10 years and several texts and monographs reflecting different aspects of the field have been published as, e.g., the detailed physics-oriented introduction of Di Francesco, Mathieu, and S´en´echal [DMS96*],1 the treatment of conformal field theories as vertex algebras by Kac [Kac98*], the development of conformal field theory in the context of algebraic geometry as in Frenkel and Ben-Zvi [BF01*] and more general by Beilinson and Drinfeld [BD04*]. There is also the comprehensive collection of articles by Deligne, Freed, Witten, and others in [Del99*] aiming to give an introduction to strings and quantum field theory for mathematicians where conformal field theory is one of the main parts of the text. The prese
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