Nondynamical four-dimensional three-form ($F_4=g_3^{2}q{\mathrm{vol}}_4$)

A three-form potential in four dimensions has no local massless polarizations. Its four-form field strength can be a constant multiple of the spacetime volume form. The equation $d(g_3^{-2}\ast F_4)=0$ leaves a constant flux parameter, which can affect vacuum energy despite supplying no local wave.