Standard quantum field theory typically models the electromagnetic vacuum on a fixedfour-manifold with no additional global topological sectors. Hertog and Hawking in recentyears made efforts to develop alternative theory. We consider a relaxation motivated byholographic/bulk-boundary ideas: observed 4D spacetime X is the base of a fibration π :Y → X with compact k-dimensional fiber Σ. Instead of invoking a derived pushforwarddirectly at the level of differential forms, we define a concrete transgression current on Xby integration along the fiber : a closed bulk (3 + k)-form eJ induces a boundary 3-formJs := π!( eJ) ∈ Ω3(X ),which is automatically conserved (dJs = 0) under mild geometric hypotheses. The effectiveMaxwell system becomesdF = 0, d ⋆ F = Jmatter + Js,equivalently d(⋆F − Js) = Jmatter. We give a gauge-invariant action principle, clarify whena Proca mass term is excluded, and outline (as clearly labelled speculation) how such acohomological source could be constrained experimentally via phase-sensitive cavity or in-terferometric measurements