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

Boundary States of D-Branes in AdS3 Based on Discrete Series