RATIONAL CONFORMAL FIELD THEORY IN FOUR DIMENSIONS

摘要

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 four space-time dimensions. We outline the results for 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 ∈ N.