CONTENTS
5.5.
5.6.
5.7.
5.8.
Rational vertex algebras
Twisted modules
Constructing new vertex algebras
Bibliographical notes
Chapter 6. Vertex Algebra Bundles
6.1.
6.2.
6.3.
6.4.
6.5.
6.6.
6.7.
Motivation
The group Aut 0
Exponentiating vector fields
Primary fields
The main construction
A flat connection on the vertex algebra bundle
Bibliographical notes
Chapter 7. Action of Internal Symmetries
7.1.
7.2.
7.3.
7.4.
Affine algebras, revisited
The general twisting property
Description of the n-point functions and modules
Bibliographical notes
Chapter 8. Vertex Algebra Bundles: Examples
8.1.
8.2.
8.3.
8.4.
8.5.
8.6.
Chapte]r
9.1.
9.2.
9.3.
9.4.
9.5.
9.6.
9.7.
The Heisenberg algebra and affine connections
The Virasoro algebra and projective connections
Kernel functions
The gauge action on the Heisenberg bundle
The affine Kac-Moody vertex algebras and connections
Bibliographical notes
9. Conformal Blocks I
Defining conformal blocks for the Heisenberg algebra
Definition of conformal blocks for general vertex algebras
Comparison of the two definitions of conformal blocks
Coinvariants for commutative vertex algebras
Twisted version of conformal blocks
Appendix. Proof of Proposition 9.3.2
Bibliographical notes
Chapter 10. Conformal Blocks II
10.1.
10.2.
10.3.
10.4.
10.5.
10.6.
Multiple points
Functoriality of conformal blocks
Chiral correlation functions
Conformal blocks in genus zero
Functional realization of Heisenberg conformal blocks
Bibliographical notes
Chapter 11. Free Field Realization I
11.1.
11.2.
11.3.
11.4.
The idea
Finite-dimensional setting
Infinite-dimensional setting
Bibliographical notes
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