  By constructing the configuration of D3-branes with D(-1)-branes as
D-instantons, we study the three-dimensional Yang-Mills Chern-Simons theory in
holography. Due to the presence of the D-instantons, the D7-branes with
discrepant embedding functions are able to be introduced in order to include
the fundamental fermions (as flavors) and the Chern-Simons term (at very low
energy) in the dual theory. The vacuum structure at zero temperature is studied
in the soliton background and it illustrates the topological phase transition
in the presence of instantons. Moreover, since the confinement/deconfinement
phase transition could be holographically identified as the Hawking-Page
transition in the bulk, we accordingly calculate the critical temperature of
the deconfinement phase transition by collecting the bulk onshell action as the
thermodynamical free energy. On the other hand, we evaluate the difference of
the entanglement entropy in slab configuration by using the RT formula since
the confinement may also be characterized by the entanglement entropy.
Altogether we find the behavior of the critical temperature is in qualitative
agreement with the behavior of the critical length determined by the
entanglement entropy which implies the entanglement entropy could indeed be a
character of the confinement in our setup and the D3-D(-1) system would be a
remarkable approach to study the three-dimensional gauge theory.
