D-brane and gauge invariance in closed string field theory

Abstract

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