  We first propose a topological term that captures the "intertwinement"
between the standard "$\sqrt{3} \times \sqrt{3}$" antiferromagnetic order (or
the so-called 120$^\circ$ state) and the "$\sqrt{12}\times \sqrt{12}$" valence
solid bond (VBS) order for spin-1/2 systems on a triangular lattice. Then using
a controlled renormalization group calculation, we demonstrate that there
exists an unfine-tuned direct continuous deconfined quantum critical point
(dQCP) between the two ordered phases mentioned above. This dQCP is described
by the $N_f = 4$ quantum electrodynamics (QED) with an emergent
PSU(4)=SU(4)/$Z_4$ symmetry only at the critical point. The topological term
aforementioned is also naturally derived from the $N_f = 4 $ QED. We also point
out that physics around this dQCP is analogous to the boundary of a $3d$
bosonic symmetry protected topological state with on-site symmetries only.
