Dynamical localization of Abelian gauge fields

We study the possibility that a consistent description of the four-dimensional photon field can arise from a model of scalar-QED in (4+2)-dimensional space-time. The existence of new dimensions other than the usual four represents one the most attractive approaches to adopt in the attempt to solve long lasting high energy as well as cosmological puzzles. However if the introduction of extra dimensions may con- stitute the natural frameowork for the construction of new effective field theories, it also opens the crucial question of explaining why as long as we can test, Universe appears truly four-dimensional. Extra dimensions need to be hidden somehow and one possibility is that Standard Model particles result localized on a four-dimensional brane embedded in a higher dimensional space-time. In the present work, we examine the possibility of localizing gauge fields by coupling the six-dimensional field to a vortex-like configuration of the charged scalar field, this represents a stable and cylindrically symmetric (along the four usual directions) solution, which carves Minkowski four dimensional space-time out of its throat. The main result is that, the gauge field components associated with the four di- mensional photon can be completely decoupled from the other fields, due to the gauge invariance of the model together with a mass hierarchy appearing between the compo- nents of the six-dimensional gauge field, which allows to set a cut-off for the admissible energies range. This procedure though, doesn’t leave the photon massless. We add to the six-dimensional Lagrangian a finely tuned mass term for the photon, in order to cancel the mass of the photon thus obtained. We assume this extra mass term coming from Higgs mechanism, introducing an auxiliary scalar field with vacuum expectation value appropriately chosen.