From the representation theory of vertex operator algebras to modular tensor categories in conformal field theory

Abstract

This is an expository article invited for the ``Commentary'' section of PNAS in connection with Y.-Z. Huang's article, ``Vertex operator algebras, the Verlinde conjecture, and modular tensor categories,'' appearing in the same issue of PNAS. Huang's solution of the mathematical problem of constructing modular tensor categories from the representation theory of vertex operator algebras is very briefly discussed, along with background material. The hypotheses of the theorems entering into the solution are very general, natural and purely algebraic, and have been verified in a wide range of familiar examples, while the theory itself is heavily analytic and geometric as well as algebraic.

latex file, 4 pages

References in corpus (2)

• Modular invariance of trace functions in orbifold theory
• Vertex operator algebras, the Verlinde conjecture and modular tensor categories

Cited by in corpus (9)

• Congruence Property In Conformal Field Theory
• Congruence Subgroups and Generalized Frobenius-Schur Indicators
• Virasoro representations and fusion for general augmented minimal models
• The fusion algebra of bimodule categories
• Tensor categories and the mathematics of rational and logarithmic conformal field theory
• Logarithmic intertwining operators and vertex operators
• Rigidity and modularity of vertex tensor categories
• Vertex operator algebras and the Verlinde conjecture
• Category $\mathcal{O}$ for the Virasoro algebra: Cohomology and Koszulity