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Braiding matrices, modular transformations and topological field theories in 2+1 dimensions

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Abstract

Relations between 3D topological field theories and rational conformal field theories are discussed. In the former framework, we can define the generalized Verlinde operators. Using these operators, we find modular transformations for conformal blocks of one point functions and two point functions on the torus. The result is generalized to higher genus. The correctness of our formulae is illustrated by some examples. We also emphasize the importance of the fusion algebra.

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Authors and Affiliations

  1. International School for Advanced Studies, I-34014, Trieste, Italy

    Miao Li

  2. International Center for Theoretical Physics, I-34100, Trieste, Italy

    Ming Yu

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  1. Miao Li
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  2. Ming Yu
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Communicated by L. Alvarez-Gaumé

Addresses after October 1, 1989: Institute of Theoretical Physics, Academia Sinica, Beijing, P. R. China

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Li, M., Yu, M. Braiding matrices, modular transformations and topological field theories in 2+1 dimensions. Commun.Math. Phys. 127, 195–224 (1990). https://doi.org/10.1007/BF02096502

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