ar X iv : h ep - t h / 05 09 10 3 v 1 1 4 Se p 20 05 FIAN / TD / 15 - 05 Secondary Fields in D > 2 Conformal Theories

We consider the secondary fields in D-dimensional space, D ≥ 3, generated by the non-abelian current and energy-momentum tensor. These fields appear in the operator product expansions j a µ (x)ϕ(0) and T µν (x)ϕ(0). The secondary fields underlie the construction proposed herein (see [1,2] for more details) and aimed at the derivation of exact solutions of conformal models in D ≥ 3. In the case of D = 2 this construction leads to the known [5] exactly solvable models based on the infinite-dimensional conformal symmetry. It is shown that for D ≥ 3 the existence of the secondary fields is governed by the existence of anomalous operator contributions (the scalar fields R j and R T of dimensions d j = d T = D − 2) into the operator product expansions j a µ j b ν and T µν T ρσ. The coupling constant between the field R j and the fundamental field is found. The fields R j and R T are shown to beget two infinite sets of secondary tensor fields of canonical dimensions D − 2 + s, where s is the tensor rank. The current and the energy-momentum tensor belong to those families, their Green functions being expressed through the Green functions of the fields R j and R T correspondingly. We demonstrate that the Ward identities give rise to the closed set of equations for the Green functions of the fields R j and R T .