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Hardcover ISBN:  9780821840887 
Product Code:  FIM/24 
List Price:  $73.00 
MAA Member Price:  $65.70 
AMS Member Price:  $58.40 
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Product Code:  FIM/24.E 
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AMS Member Price:  $55.20 
Hardcover ISBN:  9780821840887 
eBook ISBN:  9781470431501 
Product Code:  FIM/24.B 
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Book DetailsFields Institute MonographsVolume: 24; 2008; 168 ppMSC: Primary 81; 14; 17
This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces with coordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection—one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over \(\mathbb{P}^1\).
Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students and research mathematicians interested in algebraic/arithmetic geometry, theoretical physics (high energy) string theory.

Table of Contents

Chapters

Chapter 1. Riemann surfaces and stable curves

Chapter 2. Affine Lie algebras and integrable highest weight representations

Chapter 3. Conformal blocks and correlation functions

Chapter 4. Sheaf of conformal blocks

Chapter 5. Projectively flat connections

Chapter 6. Vertex operators and KZ equations


Additional Material

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This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces with coordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection—one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over \(\mathbb{P}^1\).
Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.
Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians interested in algebraic/arithmetic geometry, theoretical physics (high energy) string theory.

Chapters

Chapter 1. Riemann surfaces and stable curves

Chapter 2. Affine Lie algebras and integrable highest weight representations

Chapter 3. Conformal blocks and correlation functions

Chapter 4. Sheaf of conformal blocks

Chapter 5. Projectively flat connections

Chapter 6. Vertex operators and KZ equations