  Recently, in (Eur.Phys.J.C 80 (2020) 5, 432), the present authors obtained
general stringent conditions on the localization of fields in braneworlds by
imposing that its zero-mode must satisfy Einstein's equations (EE). Here, we
continue this study by considering free $p$-form. These fields present an
on-shell equivalency relation between a $p$-form and a $(D-p-2)$-form, provided
by Hodge duality (HD). This symmetry will impose a new consistency condition,
namely, confinement of a $p$-form must imply the localization of its dual. We
apply the above conditions to $6$D braneworlds. With this, we find that in
global string-like defects, for example, the $1$-form has a normalizable
zero-mode. By using the HD, we show that its bulk dual $3$-form also has a
normalizable zero-mode, making the confinement consistent with HD. However,
these solutions cannot be made consistent with EE, therefore, these fields must
be ruled out. In fact, by imposing both conditions, only the scalar and its
dual field can be consistently localized. In this way, all the literature so
far in which the free $1$-form is localized in codimension two models should be
reviewed. These results also point to the fact that the symmetries of the
fields can be used to verify the consistency of their localization and even
prohibit it.
