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

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.