Algebraic Structures in Euclidean and Minkowskian Two-Dimensional Conformal Field Theory

Abstract

We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sewing of surfaces, and in the Minkowskian case we describe CFT by a net of operator algebras.

21 pages, contribution to proceedings for "Non-commutative Structures in Mathematics and Physics" (Brussels, July 2008)

References in corpus (5)

• Multi-interval Subfactors and Modularity of Representations in Conformal Field Theory
• Correspondences of ribbon categories
• On $\alpha$-induction, chiral generators and modular invariants for subfactors
• Conformal Correlation Functions, Frobenius Algebras and Triangulations
• Morita classes of algebras in modular tensor categories

Cited by in corpus (1)

• Hopf algebras and finite tensor categories in conformal field theory