Introduction to Conformal Field Theory

With Applications to String Theory

By: Ralph Blumenhagen, Erik Plauschinn

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Hardcover | 31 July 2009

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280 Pages

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Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory.

Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string.

In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields.

Industry Reviews

From the reviews: "Conformal Field Theory (CFT) has found applications in string theory, statistical physics, condensed matter, and has been an inspiration for developments in pure mathemathics as well. ... It is based on a graduate course at the LMU in Munich in 2007/2008 with special emphasis on computational issues, important for applications in string theory. ... This book will be useful to graduate students interested in new mathematical developments in CFT techniques relevant for string theory." (Gert Roepstorff, Zentralblatt MATH, Vol. 1175, 2010)

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Introduction	p. 1
Basics in Conformal Field Theory	p. 5
he Conformal Group	p. 5
Conformal Invariance	p. 5
Conformal Group in d ? 3	p. 8
Conformal Group in d ? 2	p. 12
Primary Fields	p. 17
The Energy-Momentum Tensor	p. 19
Radial Quantisation	p. 20
The Operator Product Expansion	p. 23
Operator Algebra of Chiral Quasi-Primary Fields	p. 29
Conformal Ward Identity	p. 29
Two- and Three-Point Functions	p. 30
General Form of the OPE for Chiral Quasi-Primary Fields	p. 32
Normal Ordered Products	p. 37
The CFT Hilbert Space	p. 41
Simple Examples of CFTs	p. 44
The Free Boson	p. 44
The Free Fermion	p. 56
The (b,c) Ghost Systems	p. 67
Highest Weight Representations of the Virasoro Algebra	p. 70
Correlation Functions and Fusion Rules	p. 76
Non-Holomorphic OPE and Crossing Symmetry	p. 81
Fusing and Braiding Matrices	p. 84
Further Reading	p. 86
Symmetries of Conformal Field Theories	p. 87
Ka?-Moody Algebras	p. 87
The Sugawara Construction	p. 88
Highest Weight Representations of Sû(2)k	p. 92
The Sô(N)1 Current Algebra	p. 97
The Knizhnik-Zamolodchikov Equation	p. 99
Coset Construction	p. 102
W Algebras	p. 106
Further Reading	p. 111
Conformal Field Theory on the Torus	p. 113
The Modular Group of the Torus and the Partition Function	p. 114
Examples for Partition Functions	p. 120
The Free Boson	p. 120
The Free Boson on a circle	p. 120
The Free Boson on a circle of Radius R=?2k	p. 126
The Free Fermion	p. 130
The Free Boson Orbifold	p. 136
The Verlinde Formula	p. 142
The Sû(2)k Partition Functions	p. 146
Modular Invariants of Virc<1	p. 149
The Parafermions	p. 152
Simple Currents	p. 156
Additional Topics	p. 164
Asymptotic Growth of States in RCFTs	p. 164
Dilogarithm Identities	p. 166
Further Reading	p. 167
Supersymmetric Conformal Field Theory	p. 169
N=1 Superconformal Models	p. 169
N=2 Superconformal Models	p. 175
Chiral Ring	p. 181
Spectral Flow	p. 184
Coset Construction for the N ? 2 Unitary Series	p. 187
Gepner Models	p. 190
Massless Models of Gepner Models	p. 201
Further Reading	p. 203
Boundary Conformal Field Theory	p. 205
The Boson with Boundaries	p. 206
Boundary Conditions	p. 206
Partition Function	p. 211
Boundary States for the Free Boson	p. 213
Boundary Conditions	p. 214
Tree-Level Amplitudes	p. 220
Boundary States for RCFTs	p. 225
CFTs on Non-Orientable Sufraces	p. 229
Crosscap States for the Free Boson	p. 239
Crosscap States for RCFTs	p. 245
he Orientifold of the Bosonic String	p. 248
Further Reading	p. 256
Concluding Remarks	p. 257
General Books on CFT and String Theory 259
Index	p. 261
Table of Contents provided by Ingram. All Rights Reserved.

Introduction to Conformal Field Theory

With Applications to String Theory

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Hardcover

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