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Since there is not yet a fully developed S4 theory, we have to make predictions based on fairly general observations.  One of the most interesting predictions would be that electromagnetism is not a $U(1)$-gauge theory.  This is a natural prediction that comes from the observation that if we model the physical universe as a hypersurface of $S^4(1/h)$ (at any instance of time) then the normal geodesics are circles of fixed length $1/\bar{h}$.  But the ambient space is $S^4(1/h)$ rather than the total space of a principal circle bundle.  Mathematically the natural solution is to describe electromagnetism via a 1-form $A$ on $S^4(1/h)$ and the electromagnetic field strength as $F=dA$ just as one would in principal circle-bundle.  The resulting ‘electromagnetism’ is not a $U(1)$-gauge theory.  To get a geometric reason, consider uniform gauge transformations along the circle.  Such gauge transformations lead to deformations of the hypersurface $M$.  Since normal circles from different points of $M$ can intersect, intuitively gauge invariance would be possible for a restricted set of $A$.
The prediction of non-gauge invariance of electromagnetism is vague at the moment but the serious issue that must be resolved simultaneously is what four dimensional electromagnetism will mean concretely for empirical experience in the actual physical universe.  The issue is complicated by the fact that the fundamental reason a universe that has four macroscopic spatial dimensions is experienced by us as steady and three dimensional suggests that electromagnetism is a four-dimensional phenomena which we might be experiencing as a ‘$U(1)$-invariance.  In other words, there might be no ‘auxiliary $U(1)$-bundle’ for electromagnetism beyond $S^4(1/h)$.