On the vector conformal models in an arbitrary dimension

The conventional model of the gauge vector field is invariant under local conformal symmetry only in four-dimensional space ($4d$). Conformal generalization to an arbitrary dimension $d$ impossible even for free theory, differently from scalar and fermion fields. We discuss how overcome this restriction eventually construct four actions. One these models particular case previously known theory $n$-forms others are new, up our knowledge. In some invariance preserved, two new described by actions with auxiliary compensating fields, extended version one on shell equivalent last, non-analytic, purely metric version.