D-brane and Gauge Invariance in Closed String Field Theory

We construct a system of bosonic closed string field theory coupled to a D-brane. The interaction between the D-brane and closed string field is introduced using the boundary state which is a function of constant field strength $F_{\mu\nu}$ and the tilt $\theta_\mu^i$ of the D-brane. We find that the gauge invariance requirement on the system determines the $(F_{\mu\nu},\theta_\mu^i)$-dependence of the normalization factor of the boundary state as well as the form of the purely $(F_{\mu\nu},\theta_\mu^i)$ term of the action. Correspondence between the action in the present formalism and the low energy effective action (bulk + D-brane actions) in the $\sigma$-model approach is studied.