  In this paper, we obtain a gauge invariant effective action for a bulk
massless $U(1)$ gauge vector field on a brane with codimension two by using a
general Kaluza-Klein (KK) decomposition for the field. It suggests that there
exist two types of scalar KK modes to keep the gauge invariance of the action
for the massive vector KK modes. Both the vector and scalar KK modes can be
massive. The masses of the vector KK modes $m^{(n)}$ contain two parts,
$m_{1}^{(n)}$ and $m_{2}^{(n)}$, due to the existence of the two extra
dimensions. The masses of the two types of scalar KK modes $m_{\phi}^{(n)}$ and
$m_{\varphi}^{(n)}$ are related to the vector ones, i.e.,
$m_{\phi}^{(n)}=m_{1}^{(n)}$ and $m_{\varphi}^{(n)}=m_{2}^{(n)}$. Moreover, we
derive two Schr\"{o}dinger-like equations for the vector KK modes, for which
the effective potentials are just the functions of the warp factor.
