论文标题
$ u（1）$ u（1）$ gauge矢量字段的kaluza-klein模式与codimension-$ d $
Kaluza-Klein modes of $U(1)$ gauge vector field on brane with codimension-$d$
论文作者
论文摘要
从论文[JHEP 01（2019）021]中，众所周知，由于矢量kaluza-klein（kk）模式与两种类型的标量kk模式之间的耦合，因此无质量$ u（1）$ u（1）$ gauge向量场在codimension-2 brane上的有效动作是不变的。将此结果推广到具有任意数量额外维度的Brane世界模型很有趣。在这项工作中，我们首先研究了三个额外维度的情况。 KK分解后，标量KK模式有三种类型。除了这些标量模式之间的相互耦合外，标量和向量KK模式之间还存在耦合。耦合常数并非全部独立。耦合常数之间的关系使我们能够获得一个规格不变的有效作用，从中我们可以从中可以看到向量KK模式的质量取决于所有三个额外的维度。但是，标量模式的质量仅取决于三个额外维度中的两个。然后，我们将结果推广到具有Codimension $ d $（$ d = 1，2 ... $）的Branes中，发现$ D $将直接影响KK模式的质量。但是，对于巨大的向量KK模式，总是有一个规格不变的有效动作。
From the paper [JHEP 01 (2019) 021], it is known that the effective action of a massless $U(1)$ gauge vector field on a codimension-2 brane is gauge invariant due to the coupling between the vector Kaluza-Klein (KK) modes with two types of scalar KK modes. It is interesting to generalize this result to a brane world model with an arbitrary number of extra dimensions. In this work, we first investigate the case with three extra dimensions. After KK decomposition, there are three types of scalar KK modes. In addition to the mutual coupling between these scalar modes, there are also coupling between the scalar and the vector KK modes. The coupling constants are not all independent. The relationships between the coupling constants enable us to obtain a gauge invariant effective action, from which we can see that the masses of the vector KK modes depend on all the three extra dimensions. The masses of the scalar modes, however, depend only on two of the three extra dimensions. Then we generalize the results into branes with codimension $d$ ($d=1, 2...$), and find that $d$ will directly affect the masses of the KK modes. But there is always a gauge invariant effective action for the massive vector KK modes.
