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Abstract |
In this talk I will survey the results on the construction of tensor categories in conformal field theory and its connection with other mathematical results, especially operator product expansion and modular invariance, in conformal field theory. For rational and logarithmic conformal field theories, I will review the results of Huang-Lepowsky and Huang -Lepowsky-Zhang, respectively,that yield braided tensor categories, and in the rational case, my results yield modular tensor categories as well. In the case of rational conformal field theory, I will also briefly discuss the construction of the modular tensor categories for the Wess-Zumino -Novikov-Witten models and, especially, a recent discovery concerning the proof of the fundamental rigidity property of the modular tensor categories for this important special case, in relation with the works of Tsuchiya-Ueno-Yamada, Beilinson-Feigin-Mazur, Faltings, Kazhdan -Lusztig, Teleman, Finkelberg and Bakalov-Kirillov. In the case of logarithmic conformal field theory, I will mention suitable categories of modules for the triplet W-algebras as an example of the applications of the general construction of the braided tensor category structure. This talk is based on a review paper by Lepowsky and me published in Journal of Physics A. |
