Four Dimensional CFT Models with Rational Correlation Functions

Details Four Dimensional CFT Models with Rational Correlation Functions Four Dimensional CFT Models with Rational Correlation Functions

2001-10-25

arxiv.org/abs/hep-th/0110230v2

J.Phys.A35:2985-3008,2002

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture in Sec. 6 are revised. Minor errors are corrected

Scientific paper

10.1088/0305-4470/35/12/319

Recently established rationality of correlation functions in a globally conformal invariant 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 field $\phi$ of 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 of $\phi$ is shown to coincide with a simpler one, generated by a bilocal scalar field $V(x_1,x_2)$ of dimension (1,1). The modes of V together with the unit operator span an infinite dimensional Lie algebra $L_V$ 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 $L_V$) is proven to be equivalent to $c \in N$.

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