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.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 April 2005
 DOI:
 10.1073/pnas.0501135102
 arXiv:
 arXiv:math/0504311
 Bibcode:
 2005PNAS..102.5304L
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Representation Theory;
 High Energy Physics  Theory
 EPrint:
 latex file, 4 pages