p-brane Dyons, $\Theta$-terms and Dimensional Reduction

We present two novel derivations of the recently established $(-)^p$ factor in the charge quantization condition for $p$-brane dyon sources in spacetime dimension $D$=$2p$+2. The first relies on the charge shift produced by (generalized) $\theta$-terms. The second obtains this dimensional-dependent "spin flip" by compactification