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

TL;DR

This paper explores the structure of D-dimensional conformal field theories with scalar fields, introducing generalized renormalization and RG equations, revealing an infinite algebraic structure at fixed points, and deriving sum rules for operator dimensions and coefficients.

Contribution

It presents a novel generalization of renormalization and RG equations for scalar field theories in curved D-dimensional spaces, uncovering an infinite algebraic structure at conformal fixed points.

Findings

Infinite algebraic structure generated by diffeomorphism and Weyl transformations.

Sum rules for operator dimensions and Wilson coefficients derived from crossing symmetry.

Generalized renormalization procedure applicable to models with nontrivial metrics.

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.