  We provide a simple UV theory for a Dirac dark matter with a massless Abelian
gauge boson. We introduce a single fermion transforming as the $\bf{16}$
representation in the SO(10)$'$ gauge group, which is assumed to be
spontaneously broken to SU(5)$'\times$U(1)$'$. The SU(5)$'$ gauge interaction
becomes strong at an intermediate scale and then we obtain a light composite
Dirac fermion with U(1)$'$ gauge interaction at the low-energy scale. Its
thermal relic can explain the observed amount of dark matter consistently with
other cosmological and astrophysical constraints. We discuss that a nonzero
kinetic mixing between the U(1)$'$ gauge boson and the Hypercharge gauge boson
is allowed and the temperature of the visible sector and the dark matter sector
can be equal to each other.
