论文标题
$ p $ - 形式字段的一致性条件在Codimension上本地化两个Braneworlds
Consistency Conditions for $p$-Form Fields Localization on Codimension two Braneworlds
论文作者
论文摘要
最近，在（EUR.PHYS.J.C 80（2020）5，432）中，目前的作者通过强加其零模式必须满足Einstein的方程（EE），从而获得了对Braneworlds田地定位的普遍严格条件。在这里，我们通过考虑免费的$ p $ form继续这项研究。这些字段呈现出由Hodge Duality（HD）提供的$ p $ - 形式与$ P $ - 形式和$ P $（D-P-2）$的形式之间的相同性关系。这种对称性将施加新的一致性条件，即，对$ p $形式的限制必须暗示其偶的本地化。我们将上述条件应用于$ 6 $ d的Braneworlds。因此，我们发现在类似全局字符串的缺陷中，$ 1 $ - form具有可正常的零模式。通过使用HD，我们表明其散装双$ 3 $ - 形式也具有可正常的零模式，这使得与HD一致。但是，这些解决方案不能与EE一致，因此，必须排除这些领域。实际上，通过施加这两个条件，只有标量及其双重场才能始终如一地定位。通过这种方式，应审查所有免费$ 1 $形式的文献，其中应审查两个模型。这些结果还指出了一个事实，即可以使用该场的对称性来验证其定位的一致性，甚至禁止它。
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.
