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 $⟨j_{\mu }(x_1)j_{\nu }(x_2)\phi (x_3)\phi (x_4)⟩$ containing two conserved vector fields $j_{\mu }$ and two scalars $\phi$ 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.

11 pages

References in corpus (1)

• Generalized Wilson-Fisher critical points from the conformal OPE