  The deconfined quantum critical point (DQCP) between the N\'{e}el and valence
bond solid (VBS) order was originally proposed in quantum spin systems with a
local Hamiltonian. In the last few years analogues of DQCPs with nonlocal
interactions have been explored, which can lead to rich possibilities. The
nonlocal interactions can either arise from an instantaneous long range
interaction in the Hamiltonian, or from gapless modes that reside in one higher
spatial dimension. Here we consider another mechanism of generating nonlocal
interactions by coupling the DQCP to the "hot spots" of a Fermi surface. We
demonstrate that at least within a substantial energy window, the physics of
the DQCP is controlled by a new fixed point with dynamical exponent $z > 1$
