= Electric and magnetic dimensions of a form-coupled brane
{title2=$p_{\rm magnetic}=d-p_{\rm electric}-4$}
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.
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