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Introduction to Conformal Field Theory: With Applications to String Theory 2009 ed. [Kietas viršelis]

4.33/5 (10 ratings by Goodreads)
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  • Formatas: Hardback, 265 pages, aukštis x plotis: 235x155 mm, weight: 588 g, 24 Illustrations, black and white; XI, 265 p. 24 illus., 1 Hardback
  • Serija: Lecture Notes in Physics 779
  • Išleidimo metai: 31-Jul-2009
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642004490
  • ISBN-13: 9783642004490
Kitos knygos pagal šią temą:
Introduction to Conformal Field Theory: With Applications to String Theory 2009 ed.Didesnis paveikslėlis
  • Formatas: Hardback, 265 pages, aukštis x plotis: 235x155 mm, weight: 588 g, 24 Illustrations, black and white; XI, 265 p. 24 illus., 1 Hardback
  • Serija: Lecture Notes in Physics 779
  • Išleidimo metai: 31-Jul-2009
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642004490
  • ISBN-13: 9783642004490
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783642004490.html
Raktažodžiai:
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.

Recenzijos

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)

Based on a graduate course for masters students, this book provides an introduction to basic techniques for conformal field theory in two dimensions, with emphasis on applications to string theory. This book covers many aspects of conformal field theory with the intent of presenting concrete computational techniques in examples relevant for string theory. It provides an ideal resource for CFT techniques from related fields. (Si Li, Mathematical Reviews, Issue 2012 h)

1 Introduction 1
2 Basics in Conformal Field Theory 5
2.1 The Conformal Group
5
2.1.1 Conformal Invariance
5
2.1.2 Conformal Group in d greater than or = to 3
8
2.1.3 Conformal Group in d = 2
12
2.2 Primary Fields
17
2.3 The Energy—Momentum Tensor
19
2.4 Radial Quantisation
20
2.5 The Operator Product Expansion
23
2.6 Operator Algebra of Chiral Quasi-Primary Fields
29
2.6.1 Conformal Ward Identity
29
2.6.2 Two- and Three-Point Functions
30
2.6.3 General Form of the OPE for Chiral Quasi-Primary Fields
32
2.7 Normal Ordered Products
37
2.8 The CFT Hilbert Space
41
2.9 Simple Examples of CFTs
44
2.9.1 The Free Boson
44
2.9.2 The Free Fermion
56
2.9.3 The (b,c) Ghost Systems
67
2.10 Highest Weight Representations of the Virasoro Algebra
70
2.11 Correlation Functions and Fusion Rules
76
2.12 Non-Holomorphic OPE and Crossing Symmetry
81
2.13 Fusing and Braiding Matrices
84
Further Reading
86
3 Symmetries of Conformal Field Theories 87
3.1 Kac—Moody Algebras
87
3.2 The Sugawara Construction
88
3.3 Highest Weight Representations of su(2)k
92
3.4 The so(N)1 Current Algebra
97
3.5 The Knizhnik—Zamolodchikov Equation
99
3.6 Coset Construction
102
3.7 W Algebras
106
Further Reading
111
4 Conformal Field Theory on the Torus 113
4.1 The Modular Group of the Torus and the Partition Function
114
4.2 Examples for Partition Functions
120
4.2.1 The Free Boson
120
4.2.2 The Free Boson on a Circle
122
4.2.3 The Free Boson on a Circle of Radius R=squarerootof2k
126
4.2.4 The Free Fermion
130
4.2.5 The Free Boson Orbifold
138
4.3 The Verlinde Formula
142
4.4 The su(2)k Partition Functions
146
4.5 Modular Invariants of Virc less than 1
149
4.6 The Parafermions
152
4.7 Simple Currents
156
4.8 Additional Topics
164
4.8.1 Asymptotic Growth of States in RCFTs
164
4.8.2 Dilogarithm Identities
166
Further Reading
167
5 Supersymmetric Conformal Field Theory 169
5.1 N = 1 Superconformal Models
169
5.2 N = 2 Superconformal Models
175
5.3 Chiral Ring
181
5.4 Spectral Flow
184
5.5 Coset Construction for the N = 2 Unitary Series
187
5.6 Gepner Models
190
5.7 Massless Modes of Gepner Models
201
Further Reading
203
6 Boundary Conformal Field Theory 205
6.1 The Free Boson with Boundaries
206
6.1.1 Boundary Conditions
206
6.1.2 Partition Function
211
6.2 Boundary States for the Free Boson
213
6.2.1 Boundary Conditions
214
6.2.2 Tree-Level Amplitudes
220
6.3 Boundary States for RCFTs
225
6.4 CFTs on Non-Orientable Surfaces
229
6.5 Crosscap States for the Free Boson
239
6.6 Crosscap States for RCFTs
245
6.7 The Orientifold of the Bosonic String
248
Further Reading
256
Concluding Remarks 257
General Books on CFT and String Theory 259
Index 261