Abstract
We investigate the gauge invariance and localization of vector KK modes for a bulk U(1) gauge field under three kinds of localization mechanism on a brane with one extra dimension. By a general KK decomposition for the bulk U(1) gauge field, there are both vector and scalar KK modes on the brane, which couple with each other. We demonstrate that for a localization mechanism with a gauge invariant bulk action of the U(1) gauge field, the effective action of the KK modes on the brane can be formalized to gauge invariant form. However, only the massive vector KK modes and their accompanying scalar ones can be both localized on the brane, which depends on the solution of the brane, the gauge invariance of the massive vector field is finally preserved. For a localization mechanism with a broken gauge invariant bulk action of the field, it is impossible to rebuild the gauge invariance on the brane.
Highlights
It is known that if a mass term is added in the Lagrangian of a massless U(1) gauge field, the Lagrangian will be not gauge invariant
2 Gauge invariant KK modes of a free bulk U(1) gauge field In Refs. [31,32,33,34] with the general KK decomposition (1) the gauge invariance of massive vector KK modes for a free bulk U(1) gauge field in branes with codimension one or more was discussed
Through the KK decomposition (1) without any gauge fixed for the bulk U(1) gauge field, the gauge invariant effective action are both formalized as (10), only for the first case, the massive bound vector KK modes are localized on the brane accompanying with bound scalar ones, i.e., the gauge invariance is preserved
Summary
It is known that if a mass term is added in the Lagrangian of a massless U(1) gauge field, the Lagrangian will be not gauge invariant. To make the gauge invariance be preserved on the brane, whether the massive vector KK modes and their accompanying scalar ones can be localized at the same time. [31,32,33,34] with the general KK decomposition (1) the gauge invariance of massive vector KK modes for a free bulk U(1) gauge field in branes with codimension one or more was discussed.
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