On the vector conformal models in an arbitrary dimension

TL;DR

This paper explores the construction of conformally invariant vector field models in arbitrary dimensions, overcoming the known restriction that such invariance is only in four dimensions, and introduces new models with preserved gauge invariance.

Contribution

It presents novel conformal vector models in arbitrary dimensions, including models with local actions and auxiliary scalar fields, expanding the understanding of conformal invariance beyond four dimensions.

Findings

Constructed four vector conformal actions in arbitrary dimensions.

Identified models with preserved gauge invariance and auxiliary scalar fields.

Established on-shell equivalence between different formulations of the models.

Abstract

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.