Four Dimensional CFT Models with Rational Correlation Functions
Loading...
Date
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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 $ϕ$ 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 $ϕ$ 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 $c \in N$.
28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture in Sec. 6 are revised. Minor errors are corrected
28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture in Sec. 6 are revised. Minor errors are corrected