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December 2009 Infinite Lie algebras and dual pairs in 4D CFT models
Ivan Todorov
J. Phys. Math. 1: 1-12 (December 2009). DOI: 10.4303/jpm/S090601


It is known that there are no local scalar Lie fields in more than two dimensions. Bilocal fields, however, which naturally arise in conformal operator product expansions, do generate infinite Lie algebras. It is demonstrated that these Lie algebras of local observables admit (highly reducible) unitary positive energy representations in a Fock space. The multiplicity of their irreducible components is governed by a compact gauge group. The mutually commuting observable algebra and gauge group form a dual pair in the sense of Howe. In a theory of local scalar fields of conformal dimension two in four space-time dimensions the associated dual pairs are constructed and classified. The talk reviews joint work of B. Bakalov, N. M. Nikolov, K.-H. Rehren, and the author.


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Ivan Todorov. "Infinite Lie algebras and dual pairs in 4D CFT models." J. Phys. Math. 1 1 - 12, December 2009.


Published: December 2009
First available in Project Euclid: 25 October 2010

zbMATH: 1264.81274
Digital Object Identifier: 10.4303/jpm/S090601

Primary: 81T10

Keywords: dual pairs , Lie algebras , Quantum field theory

Rights: Copyright © 2009 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)


Vol.1 • December 2009
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