Four-dimensional conformal field theory models with rational correlation functions

Autor:	I. T. Todorov, Erwin Schrodinger, N. M. Nikolov
Rok vydání:	2002
Předmět:	Physics Pure mathematics Unitarity Scalar (mathematics) Minkowski space Wightman axioms Lie algebra General Physics and Astronomy Symmetric tensor Statistical and Nonlinear Physics Central charge Scalar field Mathematical Physics
Zdroj:	Journal of Physics A: Mathematical and General. 35:2985-3007
ISSN:	1361-6447 0305-4470
DOI:	10.1088/0305-4470/35/12/319
Popis:	Recently established rationality of correlation functions in a globally conformal invari- ant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider in detail a model of a neutral scalar fieldof dimension 2. It depends on a positive real parameter c, an analogue of the Virasoro central charge, and admits for all (finite) c an infinite number of conserved symmetric tensor currents. The operator product algebra ofis shown to coincide with a simpler one, generated by a bilocal scalar field V (x1, x2) of dimension (1, 1). The modes of V together with the unit operator span an infinite dimensional Lie algebra LV whose vacuum (i.e. zero energy lowest weight) representations only depend on the central charge c. Wightman positivity (i.e. unitarity of the representations of LV ) is proven to be equivalent to c ∈ N. Mathematical Subject Classification. 81T40, 81R10, 81T10
Databáze:	OpenAIRE
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