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 requires consistency of the condition under the charge shifts produced by (generalized) $\theta$-terms. The second traces the sign difference between adjoining dimensions to compactification effects.