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Classical and quantum conformal field theory

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Abstract

We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field theory, we define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish. The classical limit of the equations for the duality matrices in rational field theory together with some results of category theory, suggest that (quantum) conformal field theory should be regarded as a generalization of group theory.

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Authors and Affiliations

  1. Institute for Advanced Study, 08540, Princeton, NJ, USA

    Gregory Moore & Nathan Seiberg

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  1. Gregory Moore
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Communicated by L. Alvarez-Gaumé

On leave of absence from the Department of Physics, Weizmann Institute of Science, Rehovot 76100, Israel

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Moore, G., Seiberg, N. Classical and quantum conformal field theory. Commun.Math. Phys. 123, 177–254 (1989). https://doi.org/10.1007/BF01238857

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