String-Net Construction of RCFT Correlators

Preface
	References
Contents
1 Introduction
	1.1 A New Construction of RCFT Correlators
	1.2 Advantages of the String-Net Construction
	1.3 Organization of the Book
	References
2 Correlators in Rational Conformal Field Theory
	2.1 Open-Closed Modular Functor
	2.2 World Sheets
	2.3 Field Contents
		2.3.1 Fields in the Bulk
		2.3.2 Fields on Physical Boundaries
	2.4 Correlators as Vectors in Spaces of Conformal Blocks
	References
3 Correlators from String Nets
	3.1 String Nets
	3.2 Idempotent Completion
	3.3 The String-Net Modular Functor
	3.4 String Nets from World Sheets
	3.5 String-Net Correlators
	References
4 Correlators of Particular Interest
	4.1 Vertical Operator Product
	4.2 Horizontal Operator Products
	4.3 Bulk Algebras
	4.4 Torus Partition Function
	4.5 Boundary Operator Product
	4.6 Bulk-Boundary Operator Product
	References
5 Internal Eckmann–Hilton Relation
	5.1 An Internalized Eckmann–Hilton Argument
	5.2 Three Braided Colored Operads
	5.3 Proof of the Relation
	References
6 Outlook: Universal Correlators
	6.1 String Nets Colored by a Pivotal Bicategory
	6.2 Universal Correlators from String Nets Colored by mathcalFr(mathcalC)
	References
Appendix
A.1   Spherical Fusion Categories
A.2   Frobenius Algebras
A.3   Modules and Bimodules
A.4   Module Categories
A.5   Drinfeld Center
A.6   The Central Monad and Comonad
A.7   Coends for Generating Subcategories
A.8   Graphical Calculus for Spherical Fusion Categories
A.9   Three Useful Lemmas
Appendix  References