Four-dimensional CFT models with rational correlation functions

by I. TODOROV (Bulgarian Academy of Sciences)

Thursday 21 Feb 2002, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

Global conformal invariance in Minkowski space and Wightman axioms imply rationality of correlation functions. The most general rational SU(2,2)- invariant n-point function of a set of fields of given transformation properties depends on a finite number of parameters and is computable. This allows us to approach the existence problem for non-trivial 'rational' conformal field theory (CFT) models in 4 dimensions in a constructive way. In particular, the truncated 4-point function of a scalar field of dimension 2 depends on a single parameter c which appears as a 4D generalization of the Virasoro central charge. We prove that Wightman positivity implies that c is a positive integer. The talk will review joint work with Nikolay M. Nikolov and Yassen S. Stanev (Commun. Math. Phys. 218 (2001) 417-436 and hep-th/0110230).