文章基本信息

标题：Gauge Symmetry and Howe Duality in 4D Conformal Field Theory Models
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作者：Ivan Todorov
期刊名称：Advances in Mathematical Physics
印刷版ISSN：1687-9120
电子版ISSN：1687-9139
出版年度：2010
卷号：2010
DOI：10.1155/2010/509538
出版社：Hindawi Publishing Corporation
摘要：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.