Secondary fields and partial wave expansion. Self consistency conditions in a conformal model

TL;DR

This paper extends a method for constructing conformally invariant models from 2D to higher dimensions, analyzing four-point functions with conserved vectors and scalars to derive relationships between coupling constants.

Contribution

It generalizes a known 2D conformal model construction method to higher dimensions and establishes conditions on operator expansions for consistency.

Findings

Derived relationships between coupling constants in the model.

Identified constraints on operator content in the partial wave expansion.

Extended conformal invariance techniques to D-dimensional Euclidean space.

Abstract

A nontrivial conformally invariant model is obtained via generalization the method of obtaining conformally invariant models in $2D$ Euclidean space to the Euclidean space with dimension $D>2$. This method was previously developed by E.S. Fradkin and M.Ya. Palchik (see [7] and reference therein). The partial wave expansion of a four-point function $\langle j_{\mu}(x_{1})j_{\nu}(x_{2})\varphi(x_{3})\varphi(x_{4})\rangle$ containing two conserved vector fields $j_{\mu}$ and two scalars $\varphi$ of dimension $ d $ in a $D$ -dimensional Euclidean space is considered. The requirement of the absence the vector operator of the dimension $d + 1$ in this expansion allows us to find the relationship between all the coupling constants in such a model.