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