Renormalization Group and Infinite Algebraic Structure in D-Dimensional Conformal Field Theory

Abstract

We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations. In the fixed point the diffeomorphism and Weyl transformations generate an infinite algebraic structure of D-Dimensional conformal field theory models. The Wilson expansion and crossing symmetry enable to obtain sum rules for dimensions of composite operators and Wilson coefficients.