  We show that in (3+1)-D space-time dimensions, the O(6) non-linear sigma
model, with a level-1 Wess-Zumino-Witten term, exhibits the electromagnetic
duality. If we name the six components of the sigma field as the Neel and
valence-bond-solid (VBS) order parameters, the hedgehogs of the Neel and VBS
order play the role of monopole and charge. The duality corresponds to the
exchange of monopole and charge hence the exchange of the Neel and VBS order.
The condensation of monopole can trigger a direct Neel $\leftrightarrow$ VBS
phase transition. We conjecture that the critical point is self-dual, which is
a generalization of the deconfined quantum critical point in (2+1)-D. In this
theory, there exist two deconfined phases where the Neel/VBS hedgehogs are
massive but cost finite energy. This leads to two fractionalized phases with
particles carrying fractional spin or VBS quantum numbers and gapless gauge
bosons.
