Conformal Field Theory, Tensor Categories and Operator Algebras

Abstract

This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or quantum field theory is assumed.

Lectures notes, 66 pages: references and explanations added, typos fixed

References in corpus (7)

• Condensate induced transitions between topologically ordered phases
• Duality and defects in rational conformal field theory
• Braided tensor categories and extensions of vertex operator algebras
• Structure and Classification of Superconformal Nets
• Genera of Vertex Operator Algebras and three dimensional Topological Quantum Field Theories
• Algebraic conformal quantum field theory in perspective
• From Operator Algebras to Superconformal Field Theory

Cited by in corpus (29)

• Tensor categories for vertex operator superalgebra extensions
• Homotopy theory of algebraic quantum field theories
• Homotopical Quantum Field Theory
• Operads for algebraic quantum field theory
• Unitarity of the modular tensor categories associated to unitary vertex operator algebras, I
• Higher Structures in Algebraic Quantum Field Theory
• Towards entanglement entropy with UV cutoff in conformal nets
• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• A Remark on CFT Realization of Quantum Doubles of Subfactors. Case Index < 4
• A remark on matrix product operator algebras, anyons and subfactors
• Two-dimensional topological order and operator algebras
• Categorification of algebraic quantum field theories
• A skeletal model for 2d conformal AQFTs
• Projector Matrix Product Operators, Anyons and Higher Relative Commutants of Subfactors
• Algebraic number fields generated by Frobenius-Perron dimensions in fusion rings
• Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models
• Braided categories of endomorphisms as invariants for local quantum field theories
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• From Boolean Valued Analysis to Quantum Set Theory: Mathematical Worldview of Gaisi Takeuti
• From vertex operator superalgebras to graded-local conformal nets and back
• The Relation between Subfactors arising from Conformal Nets and the Realization of Quantum Doubles
• A characterization of a finite-dimensional commuting square producing a subfactor of finite depth
• Operator algebras and vertex operator algebras
• The quantum group dual of the first-row subcategory for the generic Virasoro VOA
• A relative tensor product of subfactors over a modular tensor category
• Loop groups and noncommutative geometry
• Quadratic $d$-numbers
• Conformal nets from minimal W-algebras
• The relative Drinfeld commutant of a fusion category and $\alpha$-induction