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Conformal Field Theory with Gauge Symmetry

Kenji Ueno Kyoto University, Kyoto, Japan
A co-publication of the AMS and Fields Institute
Available Formats:
Hardcover ISBN: 978-0-8218-4088-7
Product Code: FIM/24
List Price: $69.00 MAA Member Price:$62.10
AMS Member Price: $55.20 Electronic ISBN: 978-1-4704-3150-1 Product Code: FIM/24.E List Price:$65.00
MAA Member Price: $58.50 AMS Member Price:$52.00
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List Price: $103.50 MAA Member Price:$93.15
AMS Member Price: $82.80 Click above image for expanded view Conformal Field Theory with Gauge Symmetry Kenji Ueno Kyoto University, Kyoto, Japan A co-publication of the AMS and Fields Institute Available Formats:  Hardcover ISBN: 978-0-8218-4088-7 Product Code: FIM/24  List Price:$69.00 MAA Member Price: $62.10 AMS Member Price:$55.20
 Electronic ISBN: 978-1-4704-3150-1 Product Code: FIM/24.E
 List Price: $65.00 MAA Member Price:$58.50 AMS Member Price: $52.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$103.50 MAA Member Price: $93.15 AMS Member Price:$82.80
• Book Details

Fields Institute Monographs
Volume: 242008; 168 pp
MSC: 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.

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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 242008; 168 pp
MSC: 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.

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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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