  We study D-branes in the Lorentzian AdS_3 background from the viewpoint of
boundary states, emphasizing the role of open-closed duality in string theory.
Employing the world sheet with Lorentzian signature, we construct the Cardy
states with the discrete series. We show that they are compatible with (1)
unitarity and normalizability, and (2) the spectral flow symmetry, in the open
string spectrum. We also discuss their brane interpretation. We further show
that in the case of superstrings on AdS_3 x S^3 x T^4, our Cardy states yield
an infinite number of physical BPS states in the open string channel, on which
the spectral flows act consistently.
