Constraints on the geometry of branes from massive gauge invariant vector KK modes

We investigate the gauge invariance of massive vector Kaluza-Klein (KK) modes in different brane models with two extra dimensions. We demonstrate that some additional constraint conditions on the geometry of branes are needed in order to get the gauge invariant effective action of the KK modes. Nevertheless, not all the conditions can be satisfied by the solutions of the branes, which will break the gauge invariance. Moreover, in the branes where the conditions can meet the brane solutions, we calculate mass spectra of vector and scalar KK modes, and the results show that when only one kind of scalar KK modes is found to be massive, the gauge invariance will also be broken.
Comment: 14pages, 2 figures