Operator Algebras and Conformal Field Theory

Antony J. Wassermann
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Antony J. Wassermann: University of Cambridge, Department of Pure Mathematics and Mathematical Statistics

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 966-979 from Springer

Abstract: Abstract We report on a programme to understand unitary conformal field theory (CFT) from the point of view of operator algebras. The earlier stages of this research were carried out with Jones, following his suggestion that there might be a deeper “subfactor” explanation of the coincidence between certain braid group representations that had turned up in subfactors, statistical mechanics, and conformal field theory. (Most of our joint work appears in Section 10.) The classical additive theory of operator algebras, due to Murray and von Neumann, provides a framework for studying unitary Lie group representations, although in specific examples almost all the hard work involves a quite separate analysis of intertwining operators and differential equations. Analogously, the more recent multiplicative theory provides a powerful tool for studying the unitary representations of certain infinite–dimensional groups, such as loop groups or Diff S1. It must again be complemented by a detailed analysis of certain intertwining operators, the primary fields, and their associated differential equations.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_89

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