  Based on the gauge-gravity duality, we study the three-dimensional QCD
($\mathrm{QCD}_{3}$) and Chern-Simons theory by constructing the anisotropic
black D3-brane solution in IIB supergravity. The deformed bulk geometry is
obtained by performing a double Wick rotation and dimension reduction which
becomes an anisotropic bubble configuration exhibiting confinement in the dual
theory. And its anisotropy also reduces to a Chern-Simons term due to the
presence of the dissolved D7-branes or the axion field in bulk. Using the
bubble geometry, we investigate the the ground-state energy density, quark
potential, entanglement entropy and the baryon vertex according to the standard
methods in the AdS/CFT dictionary. Our calculation shows that the ground-state
energy illustrates degenerate to the Chern-Simons coupling coefficient which is
in agreement with the properties of the gauge Chern-Simons theory. The behavior
of the quark tension, entanglement entropy and the embedding of the baryon
vertex further implies strong anisotropy may destroy the confinement.
Afterwards, we additionally introduce various D7-branes as flavor and
Chern-Simons branes to include the fundamental matter and effective
Chern-Simons level in the dual theory. By counting their orientation, we
finally obtain the associated topological phase in the dual theory and the
critical mass for the phase transition. Interestingly the formula of the
critical mass reveals the flavor symmetry, which may relate to the chiral
symmetry, would be restored if the anisotropy increases greatly. As all of the
analysis is consistent with characteristics of quark-gluon plasma, we therefore
believe our framework provides a remarkable way to understand the features of
Chern-Simons theory, the strong coupled nuclear matter and its deconfinement
condition with anisotropy.
