Electric and magnetic dimensions of a form-coupled brane ($p_{\mathrm{magnetic}}=d-p_{\mathrm{electric}}-4$)

A $(p+1)$-form gauge potential couples electrically through its pullback to a $(p+1)$-dimensional worldvolume, whose object has $p$ spatial dimensions. Its field strength has degree $p+2$ and its magnetic dual potential has degree $d-p-3$, hence magnetic spatial dimension $d-p-4$. Electric and magnetic fluxes are integrated over linking spheres of dimensions $d-p-2$ and $p+2$, respectively. This dimensional dictionary applies when the indicated objects and dual descriptions exist; top forms need separate treatment and carry no ordinary propagating polarization.