Introduction to Conformal Field Theory: With Applications to String ...

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Lecture Notes in Physics Founding Editors: W. Beiglböck, J. Ehlers, K. Hepp, H. Weidenmüller Editorial Board R. Beig, Vienna, Austria W. Beiglböck, Heidelberg, Germany W. Domcke, Garching, Germany B.-G. Englert, Singapore U. Frisch, Nice, France F. Guinea, Madrid, Spain P. Hänggi, Augsburg, Germany W. Hillebrandt, Garching, Germany R. L. Jaffe, Cambridge, MA, USA W. Janke, Leipzig, Germany H. v. Löhneysen, Karlsruhe, Germany M. Mangano, Geneva, Switzerland J.-M. Raimond, Paris, France D. Sornette, Zurich, Switzerland S. Theisen, Potsdam, Germany D. Vollhardt, Augsburg, Germany W. Weise, Garching, Germany J. Zittartz, Köln, Germany
The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching – quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research and to serve three purposes: • to be a compact and modern up-to-date source of reference on a well-defined topic • to serve as an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas • to be a source of advanced teaching material for specialized seminars, courses and schools Both monographs and multi-author volumes will be considered for publication. Edited volumes should, however, consist of a very limited number of contributions only. Proceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic formats, the electronic archive being available at springerlink.com. The series content is indexed, abstracted and referenced by many abstracting and information services, bibliographic networks, subscription agencies, library networks, and consortia. Proposals should be sent to a member of the Editorial Board, or directly to the managing editor at Springer: Christian Caron Springer Heidelberg Physics Editorial Department I Tiergartenstrasse 17 69121 Heidelberg / Germany christian.caron@springer.com
Page 4 and 5: R. Blumenhagen E. Plauschinn Introd
Page 6 and 7: Preface These lecture notes are bas
Page 8 and 9: Contents 1 Introduction ...........
Page 10 and 11: Contents xi Concluding Remarks ....
Page 12 and 13: 2 1 Introduction phase transition i
Page 14 and 15: Chapter 2 Basics in Conformal Field
Page 16 and 17: 2.1 The Conformal Group 7 ηρσ
Page 18 and 19: 2.1 The Conformal Group 9 • The c
Page 20 and 21: 2.1 The Conformal Group 11 transfor
Page 22 and 23: 2.1 The Conformal Group z 13 ′ =
Page 24 and 25: 2.1 The Conformal Group 15 z ↦→
Page 26 and 27: 2.2 Primary Fields 17 • Since p(m
Page 28 and 29: 2.3 The Energy-Momentum Tensor 19 2
Page 30 and 31: 2.4 Radial Quantisation 21 directio
Page 32 and 33: 2.5 The Operator Product Expansion
Page 38 and 39: 2.6 Operator Algebra of Chiral Quas
Page 46 and 47: 2.7 Normal Ordered Products 37 �
Page 48 and 49: 2.7 Normal Ordered Products 39 The
Page 50 and 51: 2.8 The CFT Hilbert Space 41 togeth
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2.8 The CFT Hilbert Space 43 for n
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2.9 Simple Examples of CFTs 45 S =
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2.9 Simple Examples of CFTs 47 Let
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2.9 Simple Examples of CFTs 49 c 1
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2.9 Simple Examples of CFTs 51 The
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2.9 Simple Examples of CFTs � L0
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2.9 Simple Examples of CFTs 55 Howe
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2.9 Simple Examples of CFTs 57 γ 0
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2.9 Simple Examples of CFTs 59 Radi
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2.9 Simple Examples of CFTs 61 whic
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2.9 Simple Examples of CFTs 63 Comp
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2.9 Simple Examples of CFTs 65 �
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2.10 Highest Weight Representations
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2.11 Correlation Functions and Fusi
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2.11 Correlation Functions and Fusi
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2.12 Non-Holomorphic OPE and Crossi
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2.12 Non-Holomorphic OPE and Crossi
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2.13 Fusing and Braiding Matrices 8
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Chapter 3 Symmetries of Conformal F
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3.2 The Sugawara Construction 89 wh
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3.2 The Sugawara Construction 91 c
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3.4 The �so(N)1 Current Algebra 9
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3.5 The Knizhnik-Zamolodchikov Equa
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3.5 The Knizhnik-Zamolodchikov Equa
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3.6 Coset Construction 103 Quotient
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3.6 Coset Construction 105 Hilbert
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3.7 W Algebras 107 where the first
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3.7 W Algebras 109 However, one sti
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Further Reading 111 N (N (LL)L) CWW
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114 4 Conformal Field Theory on the
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Chapter 5 Supersymmetric Conformal
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5.1 N = 1 Superconformal Models 171
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5.3 Chiral Ring 181 primaries, the
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5.3 Chiral Ring 183 always two comp
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5.4 Spectral Flow 185 � + ′ −
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5.5 Coset Construction for the N =
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5.5 Coset Construction for the N =
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5.6 Gepner Models 191 in moduli spa
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5.6 Gepner Models 193 S �so(10)1
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5.6 Gepner Models 195 Except the tw
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5.6 Gepner Models 197 Q � state
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5.6 Gepner Models 199 Before perfor
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5.7 Massless Modes of Gepner Models
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Further Reading 203 (3, −3, 0) (2
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Chapter 6 Boundary Conformal Field
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6.1 The Free Boson with Boundaries
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6.2 Boundary States for the Free Bo
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6.3 Boundary States for RCFTs 225
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6.3 Boundary States for RCFTs 227 T
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6.4 CFTs on Non-Orientable Surfaces
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6.5 Crosscap States for the Free Bo
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6.6 Crosscap States for RCFTs 245 w
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6.6 Crosscap States for RCFTs 247
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6.7 The Orientifold of the Bosonic
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Concluding Remarks Let us conclude
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Index A A-D-E classification, 148 a
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Index 263 Klein bottle partition fu
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Index 265 simple current, 161 summa
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